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On the origins of hierarchy in complex networks
Open accessAbstract
Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological, and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that nonadaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace, using in silico evolved networks.
Checked 2026-10-07 · 1 reference not checked yet
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Written from the paper’s full text.
TL;DR
The paper defines a 3D morphospace of hierarchy using treeness, feedforwardness, and orderability, then maps 125 real networks and null models into it. It finds four major clusters, with two matching random-network expectations and two—ecological and gene networks—apparently shaped by functional constraints.
Key findings
- The morphospace Ω is defined by coordinates \(u(G)=(T,F,O)\), with perfect hierarchy at \((1,1,1)\) and a totally cyclic network at \((0,0,0)\); random homogeneous and broad networks occupy basically the same region, within the bow-tie plane \(T(G)=0\).
- Among 125 real networks across 13 classes, most fall into four clusters: metabolic, neural, linguistic, and some social networks lie in the lower bow-tie domain within the random-graph cloud; electronic circuits and software graphs form a feedforward band with \(-0.2<T(G)<0.2\); gene regulatory networks plus a kinase network show slightly positive \(T(G)\) and high \(O\); ecological flow graphs cluster around \(u(G)=(0.35,0.45,0.25)\).
- Isolated extremes include a cell lineage at \(u(G)=(0.95,1,1)\) and a small social network at \(u(G)=(-1,0.06,0.09)\).
- In silico evolution over 300 target points, three \(O\) values \(\{0.15,0.5,0.85\}\), and \(10^3\) generations showed some regions are accessible while others are inaccessible, suggesting non-adaptive processes may play a major role in shaping hierarchies.
Methods
- Directed graphs are condensed by collapsing strongly connected components into a node-weighted condensed graph \(G_C\); hierarchy is quantified by treeness \(T\) from forward/backward entropies over DAGs and leaf-removal subgraphs, feedforwardness \(F\) from path weights of cyclic modules, and orderability \(O\) as the fraction of nodes not in any cycle.
- The study analyzes 125 real networks from 13 classes and compares them with directed Erdős–Rényi, Barabási–Albert, and Callaway model ensembles; randomization uses two methods preserving either the undirected degree sequence and component structure or the directed degree sequence and component structure, with 100 replicas per network and \(4|E|\) link switches or \(20|E|\) trials.
- An evolutionary search starts from small random graphs and selects graphs minimizing Euclidean distance to target points in Ω via random link addition and deletion, with 250 replicas per target point and up to 1000 generations.
Limitations
- The paper states that the study uses a static view dominated by causal relations and does not include functionality, dynamics, or weighted structures; these are left for further work.
- The paper notes that the evolutionary algorithm’s parameters may shape the observed fitness landscape, that the experiment has high computational cost, and that small network sizes provide only a coarse-grained picture of reachability.
- The formalism assumes connected directed graphs; the Appendix states that unconnected components have no causal relation and that hierarchy loses meaning across them. Exact analytical estimates are not derived for \(F\), and the \(T\) and \(O\) random-graph estimates rely on simplifying assumptions.
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69 Own interpretation · 38 Own result · 27 Not checked yet · 13 No basis given · 7 Own method
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“They display a large central cycle, much larger than that observed in their randomized counterparts.”
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In the paper
“First, a group consisting of metabolic, neural, linguistic and some social networks is found at the lower part of the bow-tie domain, clearly embedded within the cloud of random graphs (Fig. 2d) .”
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“Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints.”
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“However, most networks fall into four clusters.”
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“Two of them match the expected from random networks with similar connectivity, thus suggesting that non-adaptive factors are at work.”
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“As shown in Fig. (2a), the larger the SCC , the lower are the values of F and O .”
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“Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified.”
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“Interestingly, randomized nets of this group show a similar behavior although with a more central position within the cloud of random nets (see Fig. (3).”
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“This co-occupation, within the bow-tie plane with T ( G ) = 0, shows that random graphs appear located right in the middle between hierarchical and antihierarchical structures, independently of the type of degree distribution of the studied models.”
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“As Fig. (2d) shows, a few isolated systems reach the boundaries of Ω: a cell lineage located at u ( G ) = (0 . 95 , 1 , 1) and a small social network located at u ( G ) = ( -1 , 0 . 06 , 0 . 09).”
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“The third group displays slightly positive values of T ( G ) and is composed of graphs with cycles of small size but with a predominant position at the feedforward structure giving rise to a very high O with variable F ( G ). These are gene regulatory networks plus a protein kinase network.”
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“These results are consistent with an exploration of the morphospace using in silico evolved networks.”
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“The second group placed at the O ( G ) ≈ 1 plane shows a narrow band of feedforward nets including electronic circuits with -0 . 2 < T ( G ) < 0 . 2 and software graphs slightly biased to negative T ( G ) values.”
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“However, the most interesting results here concerns the presence of inaccessible regions, labeled in dark red color.”
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“Here, a large region of high reachability is observed for extreme values of T but, not occupied by real networks.”
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“since, for example it is easier for small networks to display extreme configurations.”
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“In most cases real data appears to avoid the general cyclic character observed in randomized networks.”
- Also stated in: § c. Confronting real data with their randomized counterparts · p. 27 · hedged
“In general, such a trend presents a larger cyclic character in randomizations than in real networks.”
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“Positive biased values are observed in food webs and most of GRNs.”
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“On the contrary, electronic circuits show an anti hierarchical configuration ( T < 0), with a tendency to occupy slightly negative, but significant, values of T .”
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“However, when compared to randomized ensembles obtained using method b , the trend is similar to the common values observed in randomized versions.”
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“Departing from the value O ≈ 0 displayed at high connectivities, as connectivity decreases, O starts to increase but nets still aggregate around T ≈ 0 and F ≈ 0.”
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“And indeed, thanks to this approximation, we showed that not all regions are equally accessible but, instead, some regions are fairly improbable to be achieved.”
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“For low connectivities, T values tend to be closer to T = 0 but both F and O change their behavior, increasing their values to reach the region around the point T = 0 , F = 1 , O = 1.”
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“In figure (16) we plot estimates of equation (D18) and real values from an ensemble of Erdos-Renyi graph and we see that, despite the strong assumptions made, the behavior of O can be clearly predicted from the mentioned equation, providing a good insight to the behavior of such coordinate.”
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- The authors state this as an assumption: Small SCCs that can also be present within the graph represent a negligible fraction of it when compared to the size of the GSCC.
- The authors state this as an assumption: There is no correlation between in-degree and out-degree, p(k_in, k_out) approximately equals p(k_in)p(k_out).
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In the paper
“Awell established concept where such questions are addressed involves the use of a morphospace [32-36] namely a phenotype space where a small set of quantitative traits can be defined as the axes.”
What the sources say
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In the paper
“Hierarchy seems to pervade a coherent form of organization that allows reducing the costs associated to reliable information transmission [39] and to support efficient genetic and metabolic control in cellular networks [40].”
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In the paper
“Hierarchy seems to pervade complexity in both living and artificial systems.”
- Also stated in: § I. INTRODUCTION · p. 1 · hedged
“Hierarchy seems a pervasive feature of the organization of natural and artificial systems [2, 3].”
What the sources say
- Not checked yetcites [2] source
- Not checked yetcites [3]
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- Also stated in: § I. INTRODUCTION · p. 1 · hedged
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In the paper
“That implies, among other things, that they account for both bow-tie structures and feed-forward sparse webs.”
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In the paper
“But hierarchy is a polysemous word, involving order, levels, inclusion or control as possible descriptors [21], none of which captures either its complexity or the problem of its measure and origins.”
What the sources say
- Not checked yetcites [21] source
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In the paper
“Although previous work using complex networks theory has quantitatively tackled the problem [3, 4, 22-25, 27-31], some questions remain:”
What the sources say
- Not checked yetcites [3]
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In the paper
“Such deviations occur because: (a) several elements are on the top, (b) downstream elements interact horizontally or (c) feedback loops are present.”
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In the paper
“It is worth to mention that SCC detection has been shown as a powerful approach for subsystem identification [15, 42, 43] unraveling the presence of nested organizations.”
What the sources say
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In the paper
“It is worth to stress that, while O ( G ) and F ( G ) converge in their upper bound in a single value that defines the region of feedforward networks, they differ when O goes to zero.”
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In the paper
“In most real systems, signal integration requires gathering inputs from different sources, while robust processing and control requires crosstalk and feedbacks, as represented by Fig. (1d), which are often organized in a modular fashion [38].”
What the sources say
- Not checked yetcites [38] source
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In the paper
“Fifty years ago [1], Herbert Simon defined complex systems as nested hierarchical networks of components organized as interconnected modules.”
What the sources say
- Not checked yetcites [1]
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In the paper
“This is a raw indicator of the fraction of the net that can be ordered.”
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In the paper
“Some of them result from the underlying rules of network growth and change, which strongly limit the repertoire of potential designs.”
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In the paper
“It is worth to note that, connectedness may be lost during a randomization process but, as we shall see in section E 2, the randomization methods we use respect the structure of components of the graph -i.e., connectedness if it be.”
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In the paper
“It is straightforward to realize that the directed, inverted tree in which all the arrows go downwards starting from a single root naturally emerges as the graphical description of the perfect hierarchical system -see fig. (5).”
- Also stated in: § 2. Directed Acyclic Graphs · p. 12 · plain
“Lemma : Under the hallmark described (see Postulates, section B), the kind of graph G depicting the perfect hierarchy is a directed tree in which all the leafs have the same length.”
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- The authors state this as an assumption: A perfectly hierarchical system has the properties of order, reversibility, and pyramidal structure.
- Also stated in: § 2. Directed Acyclic Graphs · p. 12 · plain
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In the paper
“The GSCC will represent the largest cyclic region of the graph.”
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In the paper
“This sorting implies that a DAG can represent a more or less entangled structure of interconnected causal processes.”
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In the paper
“However, meaningful information can only be obtained from the study of a single component since it represents a unique causal structure.”
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In the paper
“The combination of O ( G ) and F ( G ) tells us how are cycles located within the net and the impact they have in the order of the structure.”
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“Layers can be identified through a backward or bottom up leaf removal ( LR b ) algorithm or through a forward or top down leaf removal ( LR f ) algorithm [33].”
What the sources say
- Not checked yetcites [33] source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It turns out that the type of graph defined above satisfies all the postulates defined in B is the graphical representation of a perfect hierarchical system.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: A perfectly hierarchical system has the properties of order, reversibility, and pyramidal structure.
In the paper
“Intuitively, we first observe that deviations from reversibility can be properly captured measuring the uncertainty in reversing a given path, a measure called topological reveresibility [3].”
What the sources say
- Not checked yetcites [3]
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The matching of random and real webs in the first two clusters suggests that their hierarchical features can be accounted for from the spontaneous correlations associated to random graphs of a given degree, indicating that the observed webs are simply the most probable ones.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Rests on an assumption: The region occupied by null models indicates where no selection pressure is at work.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A tree or, more generally, a feed-forward network will display O ( G ) = 1, in agreement to their orderable nature.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It turns out that, by definition, G C is a DAG .”
- Also stated in: § a. Condensation: Obtaining a DAG from any directed graph · p. 12 · plain
“Notice, as illustrated in figure (6) that G C is a DAG , as expected.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Also stated in: § a. Condensation: Obtaining a DAG from any directed graph · p. 12 · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The computational nature of regulatory networks and the combination of layers and cycles common to energy flows in food webs separate them from this large cluster.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Although LR f and LR b algorithms identify the same number of layers, the specific composition of every layer is not necessarily the same.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In contrast, a network which is totally cyclical would display O ( G ) = 0.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We observe that the length of the longest path of a finite DAG is always bounded.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The non-cyclic nature of such graph structures enables us to define a finite set of layers.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
In the paper
“Both biological and cultural evolution operate under a number of deep constraints [60].”
What the sources say
- Not checked yetcites [60] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is worth to note that it is mathematically possible to apply this formalism to networks containing more than one connected component.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Through the values of these coordinates we must be able to identify and properly quantify deviations from such an ideal behavior.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The dissection of G C in the above described two sequences of subgraphs will enable us to exhaustively explore the role of all layers in the further hierarchy measure.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From the coordinates of u ( G ) we can extract information about the structure of the net under the conceptual background of hierarchy presented in section B based on the concepts of order , reversibility and pyramidal structure .”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- The authors state this as an assumption: A perfectly hierarchical system has the properties of order, reversibility, and pyramidal structure.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Their T ( G ) > 0 values indicate a certain degree of pyramidal structure and the low O ( G )'s are consistent with an important role played by loops.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If the quantification of the uncertainty in reversing the paths displays a lower value than the quantification of alternatives, we say that, qualitatively, the net shows a pyramidal structure.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, we observe that these bidirectional links already introduce a symmetry within the adjacency matrix under the transpose operation and, consequently, their presence would have no impact in equation (D13) and thus the reasoning still holds.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Method B: Preserving the directed degree sequence and the component structure.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We emphasize that this independence condition among k in and k out is a very strong one, consequently, results must be seen as a rough estimation of the qualitative behavior of the GSCC .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- The authors state this as an assumption: There is no correlation between in-degree and out-degree, p(k_in, k_out) approximately equals p(k_in)p(k_out).
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such nets are thus hierarchic ( T > 0), in terms of how the causal flow is organized.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“This chart allows us to elude any assumption on the statistical behavior of the ensembles of randomized graphs.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We will focus on T and O , since the active presence of paths and cycles in the computation of F makes any rough estimation extraordinarily complex and of no practical use.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, the relation between O and F enables us to estimate how many cyclic regions are in the graph and at what point of the causal flow they are located.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Method A: Preserving the undirected degree sequence and the component structure.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is not ignored by the authors that the drastic reduction of F by increasing 〈 k 〉 is tied to the impact of SCC size affecting to the length of pathways in the condensed graph.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In addition, they provide an estimator of relevance of coordinate T , since low values of O,F indicate us that the net is mainly cyclical and that the feed-forward-like analysis provided by T is less relevant than in the case where O,F are close to 1.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This latter case would belong to the perfect antihierachical system.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. The quote only partly states this claim.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Exact calculations of the above presented values are hard and far away from the scope of this work. We therefore will present the analytic results starting from some simplifying assumptions to obtain indications on what we should expect in the case of large, sparse random networks.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The conservation of σ ( G ) makes this randomization method slightly more restrictive than the other presented above.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is easy to see that a network with a handful of nodes is more likely to give extreme values than large networks.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“It is worth to note that parameters of the evolutionary algorithm may be determinant in shaping the observed fitness landscape, thereby accelerating or slowing the convergence process to the desired target point.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“For | V | ≫ 0, this model does not ensure connectedness until values of p ≈ log( | V | ) / | V | [7].”
What the sources say
- Not checked yetcites [7]
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
No general theory that captures all features of hierarchy and its origins has been proposed yet.
“Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet.”
The paper relies on this without support.
Null models do not consider optimal designs or functional constraints.
“Since null models do not consider optimal designs or functional constraints, they provide good insights about the part of the morphospace where no selection pressure is at work.”
The paper relies on this without support.
The region occupied by null models indicates where no selection pressure is at work.
“Since null models do not consider optimal designs or functional constraints, they provide good insights about the part of the morphospace where no selection pressure is at work.”
The paper relies on this without support.
In general, neither biological nor technological webs match the feedforward pattern.
“But, in general, neither biological nor technological webs match the feedforward pattern.”
The paper relies on this without support.
The 125 real networks used are representative of natural and artificial systems.
“Here we use N n = 125 real networks encompassing 13 classes of natural and artificial systems”
The authors state this as an assumption.
Unconnected components have no causal relation of any kind, and therefore the concept of hierarchy loses any meaning for them.
“we assume that unconnected components have no causal relation of any kind and, therefore, the concept of hierarchy looses any meaning.”
The authors state this as an assumption.
A perfectly hierarchical system has the properties of order, reversibility, and pyramidal structure.
“The perfectly hierarchical system will have the following three properties: - order , - reversibility and - pyramidal structure .”
The paper relies on this without support.
Links in a directed graph describe some kind of causal relation between two elements of the set which is considered relevant for the system.
“In any directed graph, links describe some kind of causal relation between two elements of the set which is considered relevant for the system.”
The paper relies on this without support.
Rigorous and systematic confrontation of real data with their randomized counterparts elucidates much of the possible origins of the observed patterns.
“It is important to stress that the rigorous and systematic confrontation of real data with their randomized counterparts elucidates much of the possible origins of the observed patterns.”
The authors state this as an assumption.
The ensemble G_C(G) is well behaved, meaning that the averages collapse to the most probable value of a given observable.
“The first one concerns the assumption that the ensemble G C ( G ) is well behaved , which means that the averages collapse to the most probable value of a given observable.”
The authors state this as an assumption.
Small SCCs that can also be present within the graph represent a negligible fraction of it when compared to the size of the GSCC.
“if we assume that small SCC s that can be also present within the graph represent a negligible fraction of it when compared to the size of the GSCC”
The authors state this as an assumption.
There is no correlation between in-degree and out-degree, p(k_in, k_out) approximately equals p(k_in)p(k_out).
“Following [16], we know that, if there is no correlation between in and out -degrees p ( k in , k out ) ≈ p ( k in ) p ( k out ), we can estimate the size of the GSCC as:”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated major: it would touch a result — a value a result rests on, reported and recomputed p-values on opposite sides of the significance level, two passages that conflict with no sign which is right, or a cited work retracted before this paper was published.
In the paper
§ V. MORPHOSPACE ACCESSIBILITY BY DRIVEN EVOLUTION · p. 6
“The number of nodes for every graph, | V | = 50, remains constant in this process”
§ 3. The accessibility of the Morphospace: Evolution · p. 27
“The initial condition of this algorithm is defined by a population of graphs P (always single connected components), being | P | = 25, each one made of | V | = 25 nodes”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ a. Network dataset · p. 24
“Four directed lexical graph from different texts according the description in [20]:”
§ a. Network dataset · p. 24
“'Angie's Wren Xmas Tale' (Paul Auster), 'Frankenstein or the modern prometeous' (Mary Shelley),' Ulisses' (James Joyce), 'Moby dick' (Herman Melville), 'Black cat' (Edgar Allan Poe) and a fragment of the New York Times column.”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ c. Confronting real data with their randomized counterparts · p. 27
“randomization method a -where directed degree sequence is preserved”
§ b. Randomization Methods · p. 25
“Method A: Preserving the undirected degree sequence and the component structure.”
Citations
Cites
Newman, M. (2010) · doi:10.1093/acprof:oso/9780199206650.001.0001 · Cited by 6,595
Bollobás, B. (1985) · Cited by 6,196
The structure of the nervous system of the nematode Caenorhabditis elegans
White, J. G., Southgate, E., Thomson, J. N., & Brenner, S. (1986) · Philosophical Transactions of the Royal Society of London. B, Biological Sciences · doi:10.1098/rstb.1986.0056 · Cited by 5,589
A General Model for the Origin of Allometric Scaling Laws in Biology
West, G. B., Brown, J. H., & Enquist, B. J. (1997) · Science · doi:10.1126/science.276.5309.122 · Cited by 5,016
The Large-Scale Organization of Metabolic Networks
Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., & Barabási, A.-L. (2000) · Nature · doi:10.1038/35036627 · Cited by 4,972
Cytoscape 2.8: new features for data integration and network visualization
Smoot, M. E., Ono, K., Ruscheinski, J., Wang, P., & Ideker, T. (2010) · Bioinformatics · doi:10.1093/bioinformatics/btq675 · Cited by 4,770
The Architecture of Complexity
Simon, H. A. (1991) · Springer eBooks · doi:10.1007/978-1-4899-0718-9_31 · Cited by 4,479
Hierarchical Organization of Modularity in Metabolic Networks
Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N., & Barabási, A.-L. (2002) · Science · doi:10.1126/science.1073374 · Cited by 4,224
Random graphs with arbitrary degree distributions and their applications
Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.026118 · Cited by 3,675
Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., & Wiener, J. (2000) · Computer Networks · doi:10.1016/s1389-1286(00)00083-9 · Cited by 2,810
Cited by
Sorted by citations
Colloquium : Criticality and dynamical scaling in living systems
Muñoz, M. A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.031001 · Cited by 556
Structure and dynamics of core/periphery networks
Csermely, P., London, A., Wu, L.-Y., & Uzzi, B. (2013) · Journal of Complex Networks · doi:10.1093/comnet/cnt016 · Cited by 446
Operational resilience: concepts, design and analysis
Ganin, A. A., Massaro, E., Gutfraind, A., Steen, N., Keisler, J. M., Kott, A., Mangoubi, R., & Linkov, I. (2016) · Scientific Reports · doi:10.1038/srep19540 · Cited by 308
Boguñá, M., Bonamassa, I., Domenico, M. D., Havlin, S., Krioukov, D., & Serrano, M. Á. (2021) · Nature Reviews Physics · doi:10.1038/s42254-020-00264-4 · Cited by 232
Different Views of Hierarchy and Why They Matter: Hierarchy as Inequality or as Cascading Influence
Bunderson, J. S., van der Vegt, G. S., Cantimur, Y., & Rink, F. A. (2015) · Academy of Management Journal · doi:10.5465/amj.2014.0601 · Cited by 211
Heterarchies: Reconciling Networks and Hierarchies
Cumming, G. S. (2016) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2016.04.009 · Cited by 126
Structure and dynamical behavior of non-normal networks
Asllani, M., Lambiotte, R., & Carletti, T. (2018) · Science Advances · doi:10.1126/sciadv.aau9403 · Cited by 118
Dimitriadis, S. I., Salis, C. I., Tarnanas, I., & Linden, D. E. J. (2017) · Frontiers in Neuroinformatics · doi:10.3389/fninf.2017.00028 · Cited by 117
The evolutionary origins of hierarchy
Mengistu, H., Huizinga, J., Mouret, J.-B., & Clune, J. (2016) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1004829 · Cited by 115
Buldú, J. M., Busquets, J., Martínez, J. H., Herrera, J. L., Echegoyen, I., Galeano, J., & Luque, J. (2018) · Frontiers in Psychology · doi:10.3389/fpsyg.2018.01900 · Cited by 97
Avena‐Koenigsberger, A., Goñi, J., Solé, R. V., & Sporns, O. (2014) · Journal of The Royal Society Interface · doi:10.1098/rsif.2014.0881 · Cited by 97
Self-citationA Review of Information Systems Research on Online Social Networks
Berger, K., Klier, J., Klier, M., & Probst, F. (2014) · Communications of the Association for Information Systems · doi:10.17705/1cais.03508 · Cited by 89
Mixed methods analysis of enterprise social networks
Behrendt, S., Richter, A., & Trier, M. (2014) · Computer Networks · doi:10.1016/j.comnet.2014.08.025 · Cited by 85
Evolutionary aspects of reservoir computing
Seoane, L. F. (2019) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2018.0377 · Cited by 74
How directed is a directed network?
MacKay, R. S., Johnson, S., & Sansom, B. (2020) · Royal Society Open Science · doi:10.1098/rsos.201138 · Cited by 71
Constraints and spandrels of interareal connectomes
Rubinov, M. (2016) · Nature Communications · doi:10.1038/ncomms13812 · Cited by 69
A morphospace for synthetic organs and organoids: the possible and the actual
Ollé-Vila, A., Duran‐Nebreda, S., Pueyo, N. C., Montañez, R., & Solé, R. V. (2016) · Integrative Biology · doi:10.1039/c5ib00324e · Cited by 66
Self-citationNeural network organization for courtship-song feature detection in Drosophila
Baker, C. A., McKellar, C., Pang, R., Nern, A., Dorkenwald, S., Pacheco, D. A., Eckstein, N., Funke, J., Dickson, B. J., & Murthy, M. (2022) · Current Biology · doi:10.1016/j.cub.2022.06.019 · Cited by 57
Technological novelty profile and invention’s future impact
Kim, D., Cerigo, D. B., Jeong, H., & Youn, H. (2016) · EPJ Data Science · doi:10.1140/epjds/s13688-016-0069-1 · Cited by 57
Using Pareto optimality to explore the topology and dynamics of the human connectome
Avena‐Koenigsberger, A., Goñi, J., Betzel, R. F., van den Heuvel, M. P., Griffa, A., Hagmann, P., Thiran, J., & Sporns, O. (2014) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2013.0530 · Cited by 56
Self-citationContreras, J. A., Goñi, J., Risacher, S. L., Sporns, O., & Saykin, A. J. (2015) · Current Behavioral Neuroscience Reports · doi:10.1007/s40473-015-0056-z · Cited by 49
Self-citationModeling customer preferences using multidimensional network analysis in engineering design
Wang, M., Chen, W., Huang, Y. M., Contractor, N., & Fu, Y. (2016) · Design Science · doi:10.1017/dsj.2016.11 · Cited by 45
Universal scaling across biochemical networks on Earth
Kim, H., Smith, H. B., Mathis, C., Raymond, J., & Walker, S. I. (2019) · Science Advances · doi:10.1126/sciadv.aau0149 · Cited by 43
Evolving complexity: how tinkering shapes cells, software and ecological networks.
Solé, R., & Valverde, S. (2020) · Philosophical Transactions of the Royal Society B: Biological Sciences · doi:10.1098/rstb.2019.0325 · Cited by 37
Self-citationTopology of the energy landscape of sheared amorphous solids and the irreversibility transition
Regev, I., Attia, I., Dahmen, K. A., Sastry, S., & Mungan, M. (2021) · Physical review. E · doi:10.1103/physreve.103.062614 · Cited by 37
Fundamental constraints to the logic of living systems
Solé, R., Kempes, C. P., Corominas-Murtra, B., De Domenico, M., Kolchinsky, A., Lachmann, M., Libby, E., Saavedra, S., Smith, E., & Wolpert, D. (2024) · Interface Focus · doi:10.1098/rsfs.2024.0010 · Cited by 34
“This concept has been extended across disciplines, from network topology to language [31,32], and also applies to ecological systems [28,33].”
BackgroundSelf-citationHierarchical community structure in networks
Schaub, M. T., Li, J., & Peel, L. (2023) · Physical review. E · doi:10.1103/physreve.107.054305 · Cited by 39
Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?
Czégel, D., & Palla, G. (2015) · Scientific Reports · doi:10.1038/srep17994 · Cited by 33
Network Hierarchy Evolution and System Vulnerability in Power Grids
Luo, L., Han, B., & Rosas-Casals, M. (2016) · IEEE Systems Journal · doi:10.1109/jsyst.2016.2628410 · Cited by 31
Hierarchical benchmark graphs for testing community detection algorithms
Yang, Z., Perotti, J. I., & Tessone, C. J. (2017) · Physical review. E · doi:10.1103/physreve.96.052311 · Cited by 31
Synthetic development: learning to program multicellular self-organization
Toda, S., Brunger, J. M., & Lim, W. A. (2019) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2019.02.008 · Cited by 29
Hierarchical networks of scientific journals
Palla, G., Tibély, G., Mones, E., Pollner, P., & Vicsek, T. (2015) · Humanities and Social Sciences Communications · doi:10.1057/palcomms.2015.16 · Cited by 29
The Third Man: hierarchy formation in Wikipedia
Lerner, J., & Lomi, A. (2017) · Applied Network Science · doi:10.1007/s41109-017-0043-2 · Cited by 27
Cheng, C., Andrews, E. H., Yan, K., Ung, M. H., Wang, D., & Gerstein, M. (2015) · Genome biology · doi:10.1186/s13059-015-0624-2 · Cited by 27
Emergence of Hierarchical Modularity in Evolving Networks Uncovered by Phylogenomic Analysis
Caetano‐Anollés, G., Aziz, M. F., Mughal, F., Gräter, F., Koç, İ., Caetano-Anollés, K., & Caetano-Anollés, D. (2019) · Evolutionary Bioinformatics · doi:10.1177/1176934319872980 · Cited by 29
Wang, M., Chen, W., Fu, Y., & Yang, Y. G. (2015) · SAE International Journal of Materials and Manufacturing · doi:10.4271/2015-01-0468 · Cited by 27
Knowledge categorization affects popularity and quality of Wikipedia articles
Lerner, J., & Lomi, A. (2018) · PLoS ONE · doi:10.1371/journal.pone.0190674 · Cited by 29
Goekoop, R., & de Kleijn, R. (2021) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2020.12.021 · Cited by 27
Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks
Moutsinas, G., Shuaib, C., Guo, W., & Jarvis, S. A. (2021) · Scientific Reports · doi:10.1038/s41598-021-93161-4 · Cited by 28
Dissecting the role of transitivity and intransitivity on coexistence in competing species networks
Alcántara, J. M., Pulgar, M., & Rey, P. J. (2016) · Theoretical Ecology · doi:10.1007/s12080-016-0323-y · Cited by 27
Tibély, G., Pollner, P., Vicsek, T., & Palla, G. (2013) · PLoS ONE · doi:10.1371/journal.pone.0084133 · Cited by 27
Construction, comparison and evolution of networks in life sciences and other disciplines
Gysi, D. M., & Nowick, K. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2019.0610 · Cited by 25
Bogdan, P., Caetano‐Anollés, G., Jolles, A. E., Kim, H., Morris, J. T., Murphy, C. A., Royer, C. A., Snell, E. H., Steinbrenner, A. D., & Strausfeld, N. J. (2021) · Integrative and Comparative Biology · doi:10.1093/icb/icab069 · Cited by 24
Tsigdinos, S., Nikitas, A., & Bakogiannis, E. (2024) · Frontiers of Engineering Management · doi:10.1007/s42524-024-0300-x · Cited by 22
Inherent directionality explains the lack of feedback loops in empirical networks
Domínguez‐García, V., Simone Pigolotti, A., & Muñoz, M. A. (2014) · Scientific Reports · doi:10.1038/srep07497 · Cited by 22
Hierarchy in industrial structure: The cases of China and the USA
Hu, F., Zhao, S., Bing, T., & Chang, Y. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.11.083 · Cited by 22
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Combining urban scaling and polycentricity to explain socio-economic status of urban regions
Khiali-Miab, A., van Strien, M. J., Axhausen, K. W., & Grêt‐Regamey, A. (2019) · PLoS ONE · doi:10.1371/journal.pone.0218022 · Cited by 22
Cycle and flow trusses in directed networks
Takaguchi, T., & Yoshida, Y. (2016) · Royal Society Open Science · doi:10.1098/rsos.160270 · Cited by 20
Hierarchical design of mechanical metamaterials: an application on pentamode-like structures
Rodriguez, S. E., Calius, E. P., Khatibi, A. A., Orifici, A. C., & Das, R. K. (2025) · International Journal of Mechanical Sciences · doi:10.1016/j.ijmecsci.2025.110232 · Cited by 19
Duong-Tran, D. A., Abbas, K., Amico, E., Corominas‐Murtra, B., Džemidžić, M., Kareken, D. A., Ventresca, M., & Goñi, J. (2021) · Network Neuroscience · doi:10.1162/netn_a_00193 · Cited by 20
Self-citationBroken detailed balance and entropy production in directed networks
Nartallo-Kaluarachchi, R., Asllani, M., Deco, G., Kringelbach, M. L., Goriely, A., & Lambiotte, R. (2024) · Physical review. E · doi:10.1103/physreve.110.034313 · Cited by 23
The hourglass effect in hierarchical dependency networks
Sabrin, K. M., & Dovrolis, C. (2017) · Network Science · doi:10.1017/nws.2017.22 · Cited by 18
A simulated annealing algorithm for randomizing weighted networks
Milisav, F., Bazinet, V., Betzel, R. F., & Mišić, B. (2024) · Nature Computational Science · doi:10.1038/s43588-024-00735-z · Cited by 21
Facilitative interaction networks in experimental microbial community dynamics
Fujita, H., Ushio, M., Suzuki, K. T., Abe, M., Yamamichi, M., Okazaki, Y., Canarini, A., Hayashi, I., Fukushima, K., Fukuda, S., et al. (2023) · Frontiers in Microbiology · doi:10.3389/fmicb.2023.1153952 · Cited by 20
Centler, F., Günnigmann, S., Fetzer, I., & Wendeberg, A. (2020) · Microorganisms · doi:10.3390/microorganisms8020190 · Cited by 16
Non-Normal Interactions Create Socio-Economic Bubbles
Sornette, D., Lera, S. C., Lin, J., & Wu, K. (2022) · Communications Physics · doi:10.1038/s42005-023-01379-7 · Cited by 16
Zhang, Y., Wang, Z., & Wang, Y. (2016) · Briefings in Bioinformatics · doi:10.1093/bib/bbv112 · Cited by 17
Resolution of ranking hierarchies in directed networks
Letizia, E., Barucca, P., & Lillo, F. (2018) · PLoS ONE · doi:10.1371/journal.pone.0191604 · Cited by 17
Rethinking Democracy: A Systems Perspective on the Global Unrest
Shkliarevsky, G. (2015) · Systems Research and Behavioral Science · doi:10.1002/sres.2331 · Cited by 15
Souza, G. M., Bertoli, S. C., & Lüttge, U. E. (2016) · Progress in botany · doi:10.1007/978-3-319-25688-7_5 · Cited by 15
Evolution of Brains and Computers: The Roads Not Taken
Solé, R., & Seoane, L. F. (2022) · Entropy · doi:10.3390/e24050665 · Cited by 14
Self-citationRethinking road network hierarchy towards new accessibility perspectives
Tsigdinos, S., Paraskevopoulos, Y., Tzouras, P. G., Bakogiannis, E., & Vlastos, T. (2023) · Transportation research procedia · doi:10.1016/j.trpro.2023.02.162 · Cited by 14
Kumar, S., Mahajan, S., & Jain, S. (2018) · PLoS ONE · doi:10.1371/journal.pone.0203311 · Cited by 14
Khiali-Miab, A., Grêt‐Regamey, A., Axhausen, K. W., & van Strien, M. J. (2021) · City and Environment Interactions · doi:10.1016/j.cacint.2021.100078 · Cited by 14
Time evolution of the hierarchical networks between PubMed MeSH terms
Balogh, S. G., Zagyva, D., Pollner, P., & Palla, G. (2019) · PLoS ONE · doi:10.1371/journal.pone.0220648 · Cited by 16
Venegas-Aravena, P., & Cordaro, E. G. (2024) · Fractal and Fractional · doi:10.3390/fractalfract8010035 · Cited by 14
Villegas, P., Muñoz, M. A., & Bonachela, J. A. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2019.0845 · Cited by 13
Distributed Neighbor Selection in Multiagent Networks
Shao, H., Pan, L., Mesbahi, M., Xi, Y., & Li, D. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3246425 · Cited by 13
Universal hierarchical behavior of citation networks
Mones, E., Pollner, P., & Vicsek, T. (2014) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2014/05/p05023 · Cited by 14
Spatial and Performance Optimality in Power Distribution Networks
Luo, L., Pagani, G. A., & Rosas-Casals, M. (2016) · IEEE Systems Journal · doi:10.1109/jsyst.2016.2590473 · Cited by 12
A new set of cluster driven composite development indicators
Verma, A., Angelini, O., & Matteo, T. D. (2020) · EPJ Data Science · doi:10.1140/epjds/s13688-020-00225-y · Cited by 12
Glassy nature of hierarchical organizations
Zamani, M., & Vicsek, T. (2017) · Scientific Reports · doi:10.1038/s41598-017-01503-y · Cited by 11
Is information the other face of causation in biological systems?
Yurchenko, S. B. (2023) · Biosystems · doi:10.1016/j.biosystems.2023.104925 · Cited by 12
Souza, G. M., & do Amaral, M. N. (2019) · Springer eBooks · doi:10.1007/978-3-030-06128-9_10 · Cited by 11
A Multidimensional Network Approach for Modeling Customer-Product Relations in Engineering Design
Wang, M., Chen, W., Huang, Y. M., Contractor, N., & Fu, Y. (2015) · ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE) · doi:10.1115/detc2015-46764 · Cited by 10
Franke, R. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.05.063 · Cited by 10
The interhospital transfer network for very low birth weight infants in the United States
Shrestha, M., Scarpino, S. V., Edwards, E. M., Greenberg, L. T., & Horbar, J. D. (2018) · EPJ Data Science · doi:10.1140/epjds/s13688-018-0155-7 · Cited by 10
A complex network perspective on brain disease
Papo, D., & Buldú, J. M. (2025) · Biological reviews/Biological reviews of the Cambridge Philosophical Society · doi:10.1111/brv.70086 · Cited by 10
Nested interaction network enhances responsiveness in collective behavior
Zheng, Z., Tao, Y., Xiang, Y., Wang, T., Zhou, Y., Lei, X., Pan, G., & Peng, X. (2026) · Communications Physics · doi:10.1038/s42005-026-02510-0 · Cited by 9
Recruitment: A Problem of Entangled Temporal Parts
Caetano‐Anollés, G., Aziz, M. F., Mughal, F., Koç, İ., Caetano-Anollés, K., & Caetano-Anollés, D. (2022) · Frontiers in Bioscience-Landmark · doi:10.31083/j.fbl2704128 · Cited by 9
Intervality and coherence in complex networks
Domínguez‐García, V., Johnson, S., & Muñoz, M. A. (2016) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4953163 · Cited by 9
Analysis of the hierarchical structure of the B. subtilis transcriptional regulatory network
Kumar, S., Vendruscolo, M., Singh, A., Kumar, D., & Samal, A. (2015) · Molecular BioSystems · doi:10.1039/c4mb00298a · Cited by 8
Biological mechanisms underlying evolutionary origins of psychotic and mood disorders
Goto, Y., Lee, Y., Yamaguchi, Y., & Jas, E. (2016) · Neuroscience Research · doi:10.1016/j.neures.2016.04.007 · Cited by 8
Complex clinical pathways of an autoimmune disease
Palla, G., Páll, N., Horváth, A., Molnár, K., Tóth, B., Kováts, T., Surján, G., Vicsek, T., & Pollner, P. (2017) · Journal of Complex Networks · doi:10.1093/comnet/cnx031 · Cited by 8
Two faces of greedy leaf removal procedure on graphs
Zhao, J.-H., & Zhou, H. (2019) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ab2cca · Cited by 8
Robustness quantification of hierarchical complex networks under targeted failures
Bilal, K., Manzano, M., Erbad, A., Calle, E., & Khan, S. U. (2018) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2018.09.008 · Cited by 8
Feedback arcs and node hierarchy in directed networks
Zhao, J.-H., & Zhou, H.-J. (2017) · Chinese Physics B · doi:10.1088/1674-1056/26/7/078901 · Cited by 7
Generalized k -core pruning process on directed networks
Zhao, J.-H. (2017) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/aa71e0 · Cited by 7
Optimal Management of Evolving Hierarchies
Hougaard, J. L., Moreno‐Ternero, J. D., & Østerdal, L. P. (2021) · Management Science · doi:10.1287/mnsc.2021.4185 · Cited by 7
Blockmap: an interactive visualization tool for big-data networks
Frantz, T. L. (2017) · Computational and Mathematical Organization Theory · doi:10.1007/s10588-017-9252-6 · Cited by 7
Evolution of Holobiont-Like Systems: From Individual to Composed Ecological and Global Units
Matyssek, R., Lüttge, U. E., & zu Castell, W. (2022) · Progress in botany · doi:10.1007/124_2022_57 · Cited by 6
Comparing the Hierarchy of Keywords in On-Line News Portals
Tibély, G., Sousa-Rodrigues, D., Pollner, P., & Palla, G. (2016) · PLoS ONE · doi:10.1371/journal.pone.0165728 · Cited by 6
The evolutionary dynamics of metabolic protocells
Pechuan-Jorge, X., Puzio, R., & Bergman, A. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006265 · Cited by 6
Fate of Duplicated Neural Structures
Seoane, L. F. (2020) · Entropy · doi:10.3390/e22090928 · Cited by 7
NSFA: Nested Scale-Free Architecture for scalable publish/subscribe over P2P networks
Zheng, H., & Wu, J. (2016) · IEEE International Conference on Network Protocols (ICNP) · doi:10.1109/icnp.2016.7784413 · Cited by 5
Hyperbolic trees for efficient routing computation
Heszberger, Z. (2022) · The Journal of Supercomputing · doi:10.1007/s11227-022-04485-5 · Cited by 5
Caetano‐Anollés, G., & Janko, R. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.973233 · Cited by 5
The Elements of Flexibility for Task-Performing Systems
Mayer, S., Sotto, L. F. D. P., & Garcke, J. (2023) · IEEE Access · doi:10.1109/access.2023.3238872 · Cited by 7
Metadata
- Authors
- Corominas-Murtra, B., Goñi, J., Solé, R. V., & Rodríguez-Caso, C.
- Affiliations
- Institució Catalana per a la Recerca i Estudis Avancats–Complex Systems Laboratory, Universitat Pompeu Fabra, 08003 Barcelona, Spain;
- Indiana University Bloomington (US)
- Institució Catalana de Recerca i Estudis Avançats (ES)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2013-07-29
- Volume
- 110
- Issue
- 33
- Pages
- 13316-13321
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC3746874
- OpenAlex
- W2141141714
- Cited by
- 160
- References
- 79
- Citations by year
- 2026: 7 · 2025: 10 · 2024: 9 · 2023: 13 · 2022: 12 · 2021: 15 · 2020: 12 · 2019: 12 · 2018: 13 · 2017: 12 · 2016: 23 · 2015: 10 · 2014: 9 · 2013: 3
- FWCI
- 10.67
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Bioinformatics and Genomic Networks
- Keywords
- network hierarchy, complex networks, morphospace, theoretical morphology, network topology, ecological networks, gene regulatory networks, social networks, technological networks, random networks, functional constraints
- MeSH terms
- Cell Physiological Phenomena, Biological Evolution, Models, Theoretical, Social Support, Ecosystem, Gene Regulatory Networks
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-07, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-07 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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