Cited by 2,639Limits and Structures in Graph TheoryComplex Network Analysis TechniquesStochastic processes and statistical mechanics

The DOI matches its Crossref record.

Random Graphs

Bollobás, Béla·2001·Cambridge University Press eBooks

DOI 10.1017/cbo9780511814068

Open this paper in CoChat — free account

Abstract

In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdös and Rényi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.

Integrity signals

Registry

Crossref · 10.1017/cbo9780511814068

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Sorted by citations

Items 301–400 of 998

On Large Deviation Properties of Erd�s?R�nyi Random Graphs
Engel, A., Monasson, R., & Hartmann, A. K. (2004) · Journal of Statistical Physics · doi:10.1007/s10955-004-2268-6 · Cited by 61
“Random graphs have kept being an issue of tremendous interest in probability and graph theory ever since the seminal work by Erdös and Rényi(1) more than four decades ago.”
Background
An Index Calculus Algorithm for Plane Curves of Small Degree
Diem, C. (2006) · Lecture notes in computer science · doi:10.1007/11792086_38 · Cited by 60
Wherefore art thou R3579X?
Bäckström, L., Dwork, C., & Kleinberg, J. M. (2011) · Communications of the ACM · doi:10.1145/2043174.2043199 · Cited by 66
Directed random graphs with given degree distributions
Chen, N., & Olvera‐Cravioto, M. (2013) · Stochastic Systems · doi:10.1214/12-ssy076 · Cited by 60
Around Borsuk’s hypothesis
Raigorodskii, A. M. (2008) · Journal of Mathematical Sciences · doi:10.1007/s10958-008-9196-y · Cited by 60
Linear-time enumeration of maximal K-edge-connected subgraphs in large networks by random contraction
Akiba, T., Iwata, Y., & Yoshida, Y. (2013) · Proceedings of the ... ACM International Conference on Information & Knowledge Management · doi:10.1145/2505515.2505751 · Cited by 60
On the Laplacian Eigenvalues of Gn,p
Coja‐Oghlan, A. (2007) · Combinatorics Probability Computing · doi:10.1017/s0963548307008693 · Cited by 60
Anomaly Detection in Time Series of Graphs using Fusion of Graph Invariants
Park, Y., Priebe, C. E., & Youssef, A. S. (2012) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2012.2233712 · Cited by 60
Monotone properties of random geometric graphs have sharp thresholds
Goel, A., Rai, S., & Krishnamachari, B. (2005) · The Annals of Applied Probability · doi:10.1214/105051605000000575 · Cited by 65
Counting Phylogenetic Networks
McDiarmid, C., Semple, C., & Welsh, D. J. A. (2015) · Annals of Combinatorics · doi:10.1007/s00026-015-0260-2 · Cited by 59
Embedding nearly-spanning bounded degree trees
Alon, N., Krivelevich, M., & Sudakov, B. (2007) · COMBINATORICA · doi:10.1007/s00493-007-2182-z · Cited by 59
“, Chapter 8 of [6]) and it is known that for p = O(log n/n) the random graphG(n, p) a.”
Background
Universality for the Distance in Finite Variance Random Graphs
van den Esker, H., van der Hofstad, R., & Hooghiemstra, G. (2008) · Journal of Statistical Physics · doi:10.1007/s10955-008-9594-z · Cited by 59
Complex Network Measurements: Estimating the Relevance of Observed Properties
Matthieu Latapy, B., & Magnien, C. (2008) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infocom.2008.227 · Cited by 58
“If it is not, then the average distance in these graphs typically grows as log(n) log(do) [39], [40].”
The Persistence Landscape and Some of Its Properties
Bubenik, P. (2020) · Abel symposia · doi:10.1007/978-3-030-43408-3_4 · Cited by 62
Large deviations of empirical neighborhood distribution in sparse random graphs
Bordenave, C., & Caputo, P. (2014) · Probability Theory and Related Fields · doi:10.1007/s00440-014-0590-8 · Cited by 58
A Sybilproof Indirect Reciprocity Mechanism for Peer-to-Peer Networks
Landa, R., Griffin, D. P., Clegg, R. G., Mykoniati, E., & Rio, M. (2009) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infcom.2009.5061938 · Cited by 57
Ignorance Is Almost Bliss: Near-Optimal Stochastic Matching with Few Queries
Blum, A. L., Dickerson, J. P., Haghtalab, N., et al. (2020) · Operations Research · doi:10.1287/opre.2019.1856 · Cited by 58
Interorganizational Collaboration in the Hurricane Katrina Response *
Butts, C. T., Acton, R. M., & Marcum, C. S. (2012) · Journal of Social Structure · doi:10.21307/joss-2019-027 · Cited by 57
Cascading Failures on Reliability in Cyber-Physical System
Zhang, Z., An, W., & Shao, F. (2016) · IEEE Transactions on Reliability · doi:10.1109/tr.2016.2606125 · Cited by 58
“Mathematically, for a graph modeling the network, if there exists a path between a pair of nodes, the nodes are connected to each other [13].”
Background
Designing threshold networks with given structural and dynamical properties
Hagberg, A. A., Swart, P. J., & Schult, D. (2006) · Physical Review E · doi:10.1103/physreve.74.056116 · Cited by 58
Static and dynamic analysis of the Internet's susceptibility to faults and attacks
Park, S.-T., Khrabrov, A., Pennock, D. M., Lawrence, S., Giles, C. L., & Ungar, L. (2004) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infcom.2003.1209235 · Cited by 57
The Strength of Absent Ties: Social Integration via Online DatingPreprint
Ortega, J., & Hergovich, P. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3044766 · Cited by 65
“Our model is a generalization of the random graph model (Erdős and Rényi, 1959; Gilbert, 1959; for a textbook reference, see Bollobás, 2001).”
Method
How selection pressure changes the nature of social dilemmas in structured populations
Pinheiro, F. L., Santos, F. C., & Pacheco, J. M. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/7/073035 · Cited by 56
Width of percolation transition in complex networks
Kalisky, T., & Cohen, R. (2006) · Physical Review E · doi:10.1103/physreve.73.035101 · Cited by 57
The largest component in a subcritical random graph with a power law degree distribution
Janson, S. (2008) · The Annals of Applied Probability · doi:10.1214/07-aap490 · Cited by 57
“Bollobás [1]): take a set of di half-edges for each vertex i, and combine the half-edges into pairs by a uniformly random matching of the set of all half-edges (this pairing is called a configuration); each pair of half-edges is then joined to form an edge of G∗(n, (di)1 ).”
Protein interaction networks in medicine and disease
Taylor, I. W., & Wrana, J. L. (2012) · PROTEOMICS · doi:10.1002/pmic.201100594 · Cited by 57
Emergence of Small-World Anatomical Networks in Self-Organizing Clustered Neuronal Cultures
de Santos‐Sierra, D., Sendiña–Nadal, I., Leyva, I., Almendral, J. A., Anava, S., Ayali, A., Papo, D., & Boccaletti, S. (2014) · PLoS ONE · doi:10.1371/journal.pone.0085828 · Cited by 57
Sampling algorithms for pure network topologies
Airoldi, E. M., & Carley, K. M. (2005) · ACM SIGKDD Explorations Newsletter · doi:10.1145/1117454.1117457 · Cited by 57
“3.1.3 Erd¨os Random WegenerateErd¨os randomgraph(Bollob´as2001) using two algorithms.”
Influential
Thermal inclusions: how one spin can destroy a many-body localized phase
Ponte, P., Laumann, C. R., Huse, D. A., & Chandran, A. (2017) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2016.0428 · Cited by 59
Efficient crowdsourcing for multi-class labeling
Karger, D. R., Oh, S., & Shah, D. (2013) · ACM SIGMETRICS Performance Evaluation Review · doi:10.1145/2494232.2465761 · Cited by 61
Sketching Sparse Matrices, Covariances, and Graphs via Tensor Products
Dasarathy, G., Shah, P., Bhaskar, B. N., et al. (2015) · IEEE Transactions on Information Theory · doi:10.1109/tit.2015.2391251 · Cited by 56
Cavity and replica methods for the spectral density of sparse symmetric random matrices
Susca, V. A. R., Vivo, P., & Kühn, R. (2021) · SciPost Physics Lecture Notes · doi:10.21468/scipostphyslectnotes.33 · Cited by 59
Lack of Gromov-hyperbolicity in small-world networks
Shang, Y. (2012) · Open Mathematics · doi:10.2478/s11533-012-0032-8 · Cited by 48
A space-efficient parallel algorithm for computing betweenness centrality in distributed memory
Edmonds, N., Hoefler, T., & Lumsdaine, A. (2010) · International Conference on High Performance Computing (HiPC) · doi:10.1109/hipc.2010.5713180 · Cited by 55
“The diameter of the giant component G′ is O(log n) whp [7], thus calculating path counts requires O(log n) iterations each of which requires O(log n) time to reduce the writes by each of the n PUs.”
Method
Spreading dynamics on heterogeneous populations: Multitype network approach
Vázquez, A. (2006) · Physical Review E · doi:10.1103/physreve.74.066114 · Cited by 54
Percolation, Connectivity, Coverage and Colouring of Random Geometric Graphs
Balister, P., Sarkar, A., & Bollobás, B. (2008) · Bolyai Society mathematical studies · doi:10.1007/978-3-540-69395-6_2 · Cited by 55
Self-citation
ON THE VARIATIONAL PROBLEM FOR UPPER TAILS IN SPARSE RANDOM GRAPHS
Lubetzky, E., & Zhao, Y. (2014) · Cited by 55
Survival Analysis Approach to Reliability, Survivability and Prognostics and Health Management (PHM)
Ma, Z. S., & KRINGS, A. W. (2008) · Proceedings - IEEE Aerospace Conference · doi:10.1109/aero.2008.4526634 · Cited by 55
“Similarly, reliability has been studied in random graphs (e.g., Bollobás 2001, Graver and Sobel 2005).”
Background
Asymptotic equivalence and contiguity of some random graphs
Janson, S. (2009) · Random Structures and Algorithms · doi:10.1002/rsa.20297 · Cited by 55
Multi-user Collisions: Applications to Discrete Logarithm, Even-Mansour and PRINCE
Fouque, P.-A., Joux, A., & Mavromati, C. (2014) · Lecture notes in computer science · doi:10.1007/978-3-662-45611-8_22 · Cited by 54
Stability of influence maximization
He, X., & Kempe, D. (2014) · ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/2623330.2623746 · Cited by 54
Nonequilibrium thermodynamics as a gauge theory
Polettini, M. (2012) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/97/30003 · Cited by 53
Dominance network analysis provides a new framework for studying the diversity–stability relationship
Ma, Z. S., & Ellison, A. M. (2019) · Ecological Monographs · doi:10.1002/ecm.1358 · Cited by 54
Universal gap scaling in percolation
Fan, J., Meng, J., Liu, Y., et al. (2020) · Nature Physics · doi:10.1038/s41567-019-0783-2 · Cited by 54
A Low-Latency and Energy-Efficient Multimetric Routing Protocol Based on Network Connectivity in VANET Communication
Wang, X., Weng, Y., & Gao, H. (2021) · IEEE Transactions on Green Communications and Networking · doi:10.1109/tgcn.2021.3100526 · Cited by 53
Random Discrete Matrices
Vu, V. (2008) · Bolyai Society mathematical studies · doi:10.1007/978-3-540-77200-2_13 · Cited by 53
Phase transitions in cooperative coinfections: Simulation results for networks and lattices
Grassberger, P., Chen, L., Ghanbarnejad, F., et al. (2016) · Physical review. E · doi:10.1103/physreve.93.042316 · Cited by 53
A Survey of Models of the Web Graph
Bonato, A. (2005) · Lecture notes in computer science · doi:10.1007/11527954_16 · Cited by 53
The cores of random hypergraphs with a given degree sequence
Cooper, C. (2004) · Random Structures and Algorithms · doi:10.1002/rsa.20040 · Cited by 53
Resilience to Contagion in Financial NetworksPreprint
Amini, H., Rama Cont, A., & Minca, A. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1865997 · Cited by 53
Econometric Models of Network Formation
de Paula, Á. (2020) · Annual Review of Economics · doi:10.1146/annurev-economics-093019-113859
Path Ramsey Number for Random Graphs
Letzter, S. (2015) · Combinatorics Probability Computing · doi:10.1017/s0963548315000279 · Cited by 52
Self-organized energy efficient cellular networks
Samdanis, K., Kutscher, D., & Brunner, M. (2010) · IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) · doi:10.1109/pimrc.2010.5671931 · Cited by 52
A Graph-Based Model for Disconnected Ad Hoc Networks
Pellegrini, F. D., Miorandi, D., Carreras, I., et al. (2007) · doi:10.1109/infcom.2007.51 · Cited by 52
“For general properties of almost all graphs see [29, 31].”
On leader selection for performance and controllability in multi-agent systems
Clark, A., Bushnell, L. G., & Poovendran, R. (2012) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2012.6426973 · Cited by 52
“We generated an Erdos-Renyi random graph G(n, p) with n = 100 total nodes [16].”
Method
Distance distribution in random graphs and application to network exploration
Blondel, V. D., Guillaume, J., Hendrickx, J. M., et al. (2007) · Physical Review E · doi:10.1103/physreve.76.066101 · Cited by 52
Critical tipping point distinguishing two types of transitions in modular network structures
Shai, S., Kenett, D. Y., Kenett, Y. N., Faust, M., Dobson, S., & Havlin, S. (2015) · Physical Review E · doi:10.1103/physreve.92.062805 · Cited by 51
A Note on Dynamical Models on Random Graphs and Fokker–Planck Equations
Delattre, S., Giacomin, G., & Luçon, É. (2016) · Journal of Statistical Physics · doi:10.1007/s10955-016-1652-3 · Cited by 52
Interacting particle systems as stochastic social dynamics
Aldous, D. (2013) · eScholarship (California Digital Library) · Cited by 52
Emergence of symmetry in complex networks
Xiao, Y., Xiong, M., Wang, W., & Wang, H. (2008) · Physical Review E · doi:10.1103/physreve.77.066108 · Cited by 52
“The fact that large real networks are symmetric is surprising[22], since ’almost all graphs are asymmetric’[26][28].”
Background
Model-based clustering with sparse covariance matrices
Fop, M., Murphy, T. B., & Scrucca, L. (2018) · Statistics and Computing · doi:10.1007/s11222-018-9838-y · Cited by 56
Economics of malware: Epidemic risks model, network externalities and incentives
Lelarge, M. (2009) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2009.5394516 · Cited by 51
A Dirac-Type Result on Hamilton Cycles in Oriented Graphs
Kelly, L., Kühn, D., & Osthus, D. (2008) · Combinatorics Probability Computing · doi:10.1017/s0963548308009218 · Cited by 51
Incremental Subgraph Feature Selection for Graph Classification
Wang, H., Zhang, P., Xingquan Zhu, A., Tsang, I. W.-H., Chen, L., Zhang, C., & Wu, X. (2016) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2016.2616305 · Cited by 50
Learning Influence Structure in Sparse Social Networks
Ravazzi, C., Tempo, R., & Dabbene, F. (2017) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2017.2781367 · Cited by 51
On the variational problem for upper tails in sparse random graphs
Lubetzky, E., & Zhao, Y. (2016) · Random Structures and Algorithms · doi:10.1002/rsa.20658 · Cited by 51
The Invasion of the Physicists
Bonacich, P. (2004) · Social Networks · doi:10.1016/j.socnet.2004.06.002 · Cited by 51
Performance of the Eschenauer–Gligor Key Distribution Scheme Under an ON/OFF Channel
Yağan, O. (2012) · IEEE Transactions on Information Theory · doi:10.1109/tit.2012.2189353 · Cited by 50
Anatomy of a young giant component in the random graph
Ding, J., Kim, J. H., Lubetzky, E., & Peres, Y. (2010) · Random Structures and Algorithms · doi:10.1002/rsa.20342 · Cited by 50
Bi-Virus SIS Epidemics over Networks: Qualitative Analysis
Santos, A., Moura, J. M. F., & Xavier, J. (2015) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2015.2406252 · Cited by 50
“Although there is no closed form for the number of regular subnetworks on n nodes, see [19], [20], [21], reference [22] shows that, in general, for random networks in the asymptotic limit of large networks there is a high probability that it contains a regular non-trivial subnetwork.”
Background
Networking—a statistical physics perspective
Yeung, C. H., & Saad, D. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/10/103001 · Cited by 54
Fluorescence microscopy image noise reduction using a stochastically-connected random field model
Haider, S. A., Cameron, A., Siva, P. V., et al. (2016) · Scientific Reports · doi:10.1038/srep20640 · Cited by 50
Opportunities and Challenges in Wireless Sensor Networks
Haenggi, M. (2006) · CRC Press eBooks · doi:10.1201/9781420003062.ch1 · Cited by 50
Complex networks emerging from fluctuating random graphs: Analytic formula for the hidden variable distribution
Abe, S., & Stefan Thurner, A. (2005) · Physical Review E · doi:10.1103/physreve.72.036102 · Cited by 54
A NETWORK FORMATION MODEL BASED ON SUBGRAPHSPreprint
Chandrasekhar, A. G., & Jackson, M. O. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2660381 · Cited by 48
“There are also features such as the expansion properties of a network that are described by maximal eigenvalue of the adjacency matrix speaks to the speed of a diffusion process on the network (Bollobas (2001)).”
BackgroundInfluential
Counting triangles in real-world networks using projections
Tsourakakis, C. E. (2010) · Knowledge and Information Systems · doi:10.1007/s10115-010-0291-2 · Cited by 49
Order-disorder phase transition in a cliquey social network
Wołoszyn, M., Stauffer, D., & KUŁAKOWSKI, K. (2007) · The European Physical Journal B · doi:10.1140/epjb/e2007-00169-4 · Cited by 49
Optimization of Graph Clustering Inspired by Dynamic Belief Systems
Li, H., Cao, H., Feng, Y., et al. (2023) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2023.3274547 · Cited by 49
Percolation of spatially constraint networks
Li, D., Li, G., Kosmidis, K., et al. (2011) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/93/68004 · Cited by 49
Minimal and maximal characteristic path lengths in connected sociomatrices
Lovejoy, W. S., & Loch, C. H. (2003) · Social Networks · doi:10.1016/j.socnet.2003.10.001 · Cited by 49
On the complexity of the herding attack and some related attacks on hash functions
Blackburn⋆, S. R., Stinson, D. R., & Upadhyay, J. (2011) · Designs Codes and Cryptography · doi:10.1007/s10623-010-9481-x · Cited by 49
Erdos-Renyi random graphs + forest fires = self-organized criticality
Ráth, B., & Tóth, B. (2009) · Electronic Journal of Probability · doi:10.1214/ejp.v14-653 · Cited by 49
Bootstrap Percolation in Power-Law Random Graphs
Amini, H., & Fountoulakis, N. (2014) · Journal of Statistical Physics · doi:10.1007/s10955-014-0946-6 · Cited by 49
Simple and efficient local codes for distributed stable network construction
Michail, O., & Spirakis, P. G. (2015) · Distributed Computing · doi:10.1007/s00446-015-0257-4 · Cited by 52
On Inductive–Transductive Learning With Graph Neural Networks
Ciano, G., Rossi, A., Bianchini, M., & Scarselli, F. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3054304 · Cited by 55
Max-matching diversity in OFDMA systems
Bai, B. B., Chen, W., Cao, Z., et al. (2010) · IEEE Transactions on Communications · doi:10.1109/tcomm.2010.04.080478 · Cited by 49
General clique percolation in random networks
Fan, J., & Chen, X. (2014) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/107/28005 · Cited by 48
Full Connectivity: Corners, Edges and Faces
Coon, J. P., Dettmann, C. P., & Georgiou, O. (2012) · Journal of Statistical Physics · doi:10.1007/s10955-012-0493-y · Cited by 48
Covid-19 and Flattening the Curve: A Feedback Control Perspective
Lauro, F. D., Kiss, I. Z., Rus, D. L., & Santina, C. D. (2020) · IEEE Control Systems Letters · doi:10.1109/lcsys.2020.3039322 · Cited by 44
Threshold Key-Establishment in Distributed Sensor Networks Using a Multivariate Scheme
Delgosha, F., & Fekri, F. (2006) · doi:10.1109/infocom.2006.258 · Cited by 48
Building Heterogeneous Peer-to-Peer Networks: Protocol and Analysis
Kwong, K.-W., & Tsang, D. H. K. (2008) · IEEE/ACM Transactions on Networking · doi:10.1109/tnet.2007.899026 · Cited by 48
Non-Hyperbolicity of Random Graphs with Given Expected Degrees
Shang, Y. (2013) · Stochastic Models · doi:10.1080/15326349.2013.838510 · Cited by 40
Forward Correction and Fountain Codes in Delay-Tolerant Networks
Altman, E., & Pellegrini, F. D. (2010) · IEEE/ACM Transactions on Networking · doi:10.1109/tnet.2010.2091968 · Cited by 47
Robustness of complex networks with implications for consensus and contagion
Zhang, H., & Sundaram, S. (2012) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2012.6425841 · Cited by 53
How Clustering Affects Epidemics in Random Networks
Coupechoux, É., & Lelarge, M. (2014) · Advances in Applied Probability · doi:10.1239/aap/1418396240 · Cited by 47
“This model is usually called the configuration model [5].”
BackgroundMethodInfluential
Accelerating Quantum Approximate Optimization Algorithm using Machine Learning
Alam, M., Saki, A. A., & Ghosh, S. (2020) · Design, Automation, and Test in Europe · doi:10.23919/date48585.2020.9116348 · Cited by 46
Phase transition in the link weight structure of networks
Mieghem, P. V., & Magdalena, S. M. (2005) · Physical Review E · doi:10.1103/physreve.72.056138 · Cited by 46
Mobility profile based routing within intermittently connected mobile ad hoc networks (ICMAN)
Ghosh, J., Ngo, H. Q., & Qiao, C. (2006) · International Conference on Wireless Communications and Mobile Computing · doi:10.1145/1143549.1143659 · Cited by 46
Random matrix analysis of localization properties of gene coexpression network
Jalan, S., Solymosi, N., Vattay, G., & Li, B. (2010) · Physical Review E · doi:10.1103/physreve.81.046118 · Cited by 44
Modular networks emerge from multiconstraint optimization
Pan, R. K., & Sitabhra Sinha, A. (2007) · Physical Review E · doi:10.1103/physreve.76.045103 · Cited by 47

Authors: Bollobás, B.
Affiliations: University of Memphis (US)
Corresponding author: Bollobás, Béla
ORCID: Bollobás, Béla
Venue: Cambridge University Press eBooks
Publisher: Cambridge University Press
Published: 2001-08-30
DOI: 10.1017/cbo9780511814068
OpenAlex: W390146837
Cited by: 2,639
References: 0
Citations by year: 2026: 37 · 2025: 68 · 2024: 79 · 2023: 82 · 2022: 126 · 2021: 136 · 2020: 137 · 2019: 111 · 2018: 108 · 2017: 138 · 2016: 138 · 2015: 129 · 2014: 136 · 2013: 135 · 2012: 151
FWCI: 6.29
Type: book
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified, 3498 d)
Locations: Cambridge University Press eBooks (publishedVersion)
Topics: Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Limits and Structures in Graph Theory
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
Keywords: random graphs, Erdős-Rényi random graphs, degree sequences, probabilistic combinatorics, random structures, graph enumeration

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.

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 ›

Are you an author, or do you see a problem with this page? Request a review

Random Graphs

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cited by

Related

Metadata

Record

About these checks