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 501–600 of 998

Conductance and congestion in power law graphs
Gkantsidis, C., Mihail, M., & Saberi, A. (2003) · ACM SIGMETRICS Performance Evaluation Review · doi:10.1145/885651.781046 · Cited by 35
Analysing the first case of the International Criminal Court from a network-science perspective
Tarissan, F., & Nollez-Goldbach, R. (2016) · Journal of Complex Networks · doi:10.1093/comnet/cnw002 · Cited by 34
Two Hardness Results on Feedback Vertex Sets
Jiang, W., Liu, T., Ren, T., et al. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-21204-8_26 · Cited by 34
“They are also called the Erdős-Rényi random graphs and have been extensively investigated [4,26].”
Background
Erdős–Ko–Rado in Random Hypergraphs
Balogh, J., Bohman, T., & Mubayi, D. (2009) · Combinatorics Probability Computing · doi:10.1017/s0963548309990253 · Cited by 32
Robustness of graph properties
Sudakov, B. (2017) · Cambridge University Press eBooks · doi:10.1017/9781108332699.009 · Cited by 37
Individual preventive social distancing during an epidemic may have negative population-level outcomes
Leung, K. Y., Ball, F., Sirl, D., et al. (2018) · Journal of The Royal Society Interface · doi:10.1098/rsif.2018.0296 · Cited by 34
“Recently, such models have started to receive more attention, and important advances have been made to gain understanding of the effect of different behavioural changes on epidemic dynamics [7-10].”
Background
Extremal eigenvalues of critical Erdős–Rényi graphs
Alt, J., Ducatez, R., & Knowles, A. (2021) · The Annals of Probability · doi:10.1214/20-aop1483 · Cited by 34
Echo state network models for nonlinear Granger causality
Duggento, A., Guerrisi, M., & Toschi, N. (2021) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2020.0256 · Cited by 34
Social Networks and the Process of Globalization
Duernecker, G., & Vega‐Redondo, F. (2017) · The Review of Economic Studies · doi:10.1093/restud/rdx054 · Cited by 34
“…main point to note here is two-fold: (a) the diameter of the largest component of a Binomial network – the so-called giant component – grows at the order of logn (see Bollobás (2001)); (b) the function Φ̂(· ; α) depends on z only through the uniquely induced distribution of component sizes.”
Background
Cluster Identification in Nearest-Neighbor Graphs
Maier, M., Hein, M., & von Luxburg, U. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-75225-7_18 · Cited by 34
Influence of the network structure on robustness
Jamakovic, A., & Uhlig, S. (2007) · The ... IEEE International Conference on Networks/The IEEE International Conference on Networks · doi:10.1109/icon.2007.4444099 · Cited by 34
Joint problem of power optimal connectivity and coverage in wireless sensor networks
Yener, B., Magdon‐Ismail, M., & Sivrikaya, F. (2006) · Wireless Networks · doi:10.1007/s11276-006-5875-0 · Cited by 34
Rescuing Tit-for-Tat with Source Coding
Locher, T., Schmid, S., & Wattenhofer, R. P. (2007) · IEEE International Conference on Peer-to-Peer Computing (P2P) · doi:10.1109/p2p.2007.10 · Cited by 34
Chunk Distribution in Mesh-Based Large-Scale P2P Streaming Systems: A Fluid Approach
da Silva, A. P. C., Leonardi, E., Mellia, M., et al. (2010) · IEEE Transactions on Parallel and Distributed Systems · doi:10.1109/tpds.2010.63 · Cited by 34
“Each chunk is distributed along a “spanning tree,” which is dynamically determined, thus enabling most peers to actively contribute their outgoing bandwidth.”
Background
Spectra of modular and small-world matrices
Kühn, R., & van Mourik, J. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/16/165205 · Cited by 34
“[1], or [2, 3, 4] for recent reviews), as well as concurrent intensive studies in spectral properties of sparse random matrices [2, 5, 6, 7, 8], the latter providing one of the key tools to study properties of the former.”
Background
Random Graphs and Branching Processes
Bollobás, B., & Riordan, O. M. (2008) · Bolyai Society mathematical studies · doi:10.1007/978-3-540-69395-6_1 · Cited by 34
Self-citation
Structural Data De-Anonymization: Theory and Practice
Ji, S., Li, W., Srivatsa, M., et al. (2016) · IEEE/ACM Transactions on Networking · doi:10.1109/tnet.2016.2536479 · Cited by 34
The clustering coefficient and the diameter of small-world networks
Gu, L., Huang, H. L., & Zhang, X. D. (2012) · Acta Mathematica Sinica English Series · doi:10.1007/s10114-012-0387-6 · Cited by 33
The Degree Sequence of Random Graphs from Subcritical Classes
Bernasconi, N., Παναγιώτου, Κ., & Steger, A. (2009) · Combinatorics Probability Computing · doi:10.1017/s0963548309990368 · Cited by 33
Efficient universal recovery in broadcast networks
Courtade, T. A., & Wesel, R. D. (2010) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2010.5707096 · Cited by 33
Functional limit theorems for random regular graphs
Dumitriu, I., Johnson, T., Pal, S., et al. (2012) · Probability Theory and Related Fields · doi:10.1007/s00440-012-0447-y · Cited by 33
Tensor Graph Convolutional Networks for Multi-Relational and Robust Learning
Ioannidis, V. N., Marques, A. G., & Giannakis, G. B. (2020) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2020.3028495 · Cited by 33
On the Geometrical Characteristic of Wireless Ad-Hoc Networks and its Application in Network Performance Analysis
Fan, P., Li, G., Cai, K., et al. (2007) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2007.348322 · Cited by 33
Distance distribution in configuration-model networks
Nitzan, M., Katzav, E., Kühn, R., et al. (2016) · Physical review. E · doi:10.1103/physreve.93.062309 · Cited by 33
Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks
Cai, C.-R., Wu, Z.-X., & Guan, J. (2014) · Physical Review E · doi:10.1103/physreve.90.052803 · Cited by 33
“[40] B.”
Hyperbrain features of team mental models within a juggling paradigm: a proof of concept
Filho, E., Bertollo, M., Tamburro, G., Schinaia, L., Chatel-Goldman, J., di Fronso, S., Robazza, C., & Comani, S. (2016) · PeerJ · doi:10.7717/peerj.2457 · Cited by 36
“In formal terms, a small-world network has a similar characteristic path length L but a greater mean clustering coefficient C than an equivalent random graph with the same number of nodes and edges (Bollobas, 2001; Watts & Strogatz, 1998).”
Background
Bridges in complex networks
Wu, A.-K., Tian, L., & Liu, Y. (2018) · Physical review. E · doi:10.1103/physreve.97.012307 · Cited by 33
Independent sets in tensor graph powers
Alon, N., & Lubetzky, E. (2006) · Journal of Graph Theory · doi:10.1002/jgt.20194 · Cited by 33
On the editing distance of graphs
Axenovich, M., Kézdy, A. E., & Martin, R. R. (2008) · Journal of Graph Theory · doi:10.1002/jgt.20296 · Cited by 33
The Sound of Many Funds Rebalancing
Chinco, A., & Fos, V. (2021) · The Review of Asset Pricing Studies · doi:10.1093/rapstu/raab009 · Cited by 33
On antimagic directed graphs
Hefetz, D., Mütze, T., & Schwartz, J. (2009) · Journal of Graph Theory · doi:10.1002/jgt.20451 · Cited by 33
Fault tolerant deployment and topology control in wirelessad hocnetworks
Li, X., Wan, P., Wang, Y., et al. (2004) · Wireless Communications and Mobile Computing · doi:10.1002/wcm.161 · Cited by 33
Self Organized Network Management Functions for Energy Efficient Cellular Urban Infrastructures
Samdanis, K., Taleb, T., Kutscher, D., et al. (2011) · Mobile Networks and Applications · doi:10.1007/s11036-011-0293-7 · Cited by 32
Zero-One Laws for Connectivity in Inhomogeneous Random Key Graphs
Yağan, O. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2574742 · Cited by 32
Outliers in spectrum of sparse Wigner matrices
Tikhomirov, K. E., & Youssef, P. (2020) · Random Structures and Algorithms · doi:10.1002/rsa.20982 · Cited by 32
A Pliable Index Coding Approach to Data Shuffling
Song, L., Fragouli, C., & Zhao, T. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2954338 · Cited by 32
Communities, clustering phase transitions, and hysteresis: Pitfalls in constructing network ensembles
Foster, D., Foster, J. G., Paczuski, M., & Grassberger, P. (2010) · Physical Review E · doi:10.1103/physreve.81.046115 · Cited by 32
Rumor spreading in random evolving graphs
Clementi, A. E. F., Crescenzi, P., Doerr, C., et al. (2015) · Random Structures and Algorithms · doi:10.1002/rsa.20586 · Cited by 32
Dynamical networks: interplay of topology, interactions and local dynamics
Afraimovich, V., & Bunimovich, L. (2007) · Nonlinearity · doi:10.1088/0951-7715/20/7/011 · Cited by 32
Symmetry in Complex Networks
Garrido, Á. (2011) · Symmetry · doi:10.3390/sym3010001 · Cited by 33
Take a Deep Breath: A Stealthy, Resilient and Cost-Effective Botnet Using Skype
Nappa, A., Fattori, A., Balduzzi, M. `., Dell’Amico, M., & Cavallaro, L. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-14215-4_5 · Cited by 30
“In an ER graph [8], for a large number of nodes n, a giant component (i.”
Background
A precise analysis of Cuckoo hashing
Drmota, M., & Kutzelnigg, R. (2012) · ACM Transactions on Algorithms · doi:10.1145/2151171.2151174 · Cited by 30
The Critical Phase for Random Graphs with a Given Degree Sequence
Kang, M., & Seierstad, T. G. (2007) · Combinatorics Probability Computing · doi:10.1017/s096354830700867x · Cited by 32
The probability that a random multigraph is simple. II
Janson, S. (2014) · Journal of Applied Probability · doi:10.1239/jap/1417528471 · Cited by 32
Hamiltonicity thresholds in Achlioptas processes
Krivelevich, M., Lubetzky, E., & Sudakov, B. (2010) · Random Structures and Algorithms · doi:10.1002/rsa.20302 · Cited by 32
Bubblestorm
Terpstra, W. W., Kangasharju, J., Leng, C., & Buchmann, A. (2007) · ACM SIGCOMM Computer Communication Review · doi:10.1145/1282427.1282387 · Cited by 32
Lifshitz tails for spectra of Erdős–Rényi random graphs
Khorunzhiy, O., Kirsch, W., & Müller, P. (2006) · The Annals of Applied Probability · doi:10.1214/1050516000000719 · Cited by 32
Equivalence of a random intersection graph and G ( n , p )
Rybarczyk, K. (2010) · Random Structures and Algorithms · doi:10.48550/arxiv.0910.5311 · Cited by 31
Spectral analysis of protein-protein interactions inDrosophila melanogaster
Kamp, C., & Christensen, K. (2005) · Physical Review E · doi:10.1103/physreve.71.041911 · Cited by 31
Perfect matchings in random intersection graphs
Bloznelis, M., & Łuczak, T. (2012) · Acta Mathematica Academiae Scientiarum Hungaricae · doi:10.1007/s10474-012-0266-8 · Cited by 30
Connectivity properties of large-scale sensor networks
Pishro-Nik, H., Chan, K., & Fekri, F. (2009) · Wireless Networks · doi:10.1007/s11276-009-0179-9 · Cited by 31
Thresholding normally distributed data creates complex networks
Cantwell, G. T., Liu, Y., Maier, B. F., et al. (2020) · Physical review. E · doi:10.1103/physreve.101.062302 · Cited by 31
On the chromatic number of random geometric graphs
McDiarmid, C., & Müller, T. (2011) · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · Cited by 31
SPECTRUM OF MARKOV GENERATORS ON SPARSE RANDOM GRAPHS
Bordenave, C., Caputo, P., & Chafaï, D. (2014) · Cited by 31
Hypergraph Similarity Measures
Surana, A., Chen, C., & Rajapakse, I. (2022) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2022.3217185 · Cited by 37
The Existence and Efficient Construction of Large Independent Sets in General Random Intersection Graphs
Nikoletseas, S., Raptopoulos, C., & Spirakis, P. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-27836-8_86 · Cited by 32
Scale-free models for the structure of business firm networks
Kitsak, M., Riccaboni, M., Havlin, S., Fabio Pammolli, A., & Stanley, E. (2010) · Physical Review E · doi:10.1103/physreve.81.036117 · Cited by 28
Behavior Evolution and Event-Driven Growth Dynamics in Social Networks
Qiu, B., Ivanova, K., Yen, J., & Liu, P. (2010) · doi:10.1109/socialcom.2010.38 · Cited by 32
Packing hamilton cycles in random and pseudo‐random hypergraphs
FRIEZE, A. M., & Krivelevich, M. (2012) · Random Structures and Algorithms · doi:10.1002/rsa.20396 · Cited by 31
CrowdSelect
Qiu, C., Squicciarini, A., Carminati, B., Caverlee, J., & Khare, D. R. (2016) · ACM International Conference on Information and Knowledge Management (CIKM) · doi:10.1145/2983323.2983830 · Cited by 32
Preferential selection based on degree difference in the spatial prisoner's dilemma games
Huang, C., Dai, Q., Cheng, H., & Li, H. (2017) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/120/18001 · Cited by 31
Large Kr‐free subgraphs in Ks‐free graphs and some other Ramsey‐type problems
Sudakov, B. (2004) · Random Structures and Algorithms · doi:10.1002/rsa.20035 · Cited by 31
Criticality on networks with topology-dependent interactions
Giuraniuc, C. V., Hatchett, J. P. L., Indekeu, J. O., et al. (2006) · Physical Review E · doi:10.1103/physreve.74.036108 · Cited by 31
High capacity, small world associative memory models
Davey, N., Calcraft, L., & Adams, R. (2006) · Connection Science · doi:10.1080/09540090600639339 · Cited by 31
“There is a long history of research into the properties of random graphs, graphs in which the connectivity matrix is randomly configured, often with a specific probability of connectivity (Bollobas, 2001).”
Background
0 RANDOM GROUPS ARISING AS GRAPH PRODUCTSPreprint
Charney, R. M., & Färber, M. (2016) · Cited by 31
Rumor Spreading in Random Evolving Graphs
Clementi, A. E. F., Crescenzi, P., Doerr, C., et al. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-40450-4_28 · Cited by 30
Feedback Message Passing for Inference in Gaussian Graphical Models
Liu, Y., Chandrasekaran, V., Anandkumar, A., et al. (2012) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2012.2195656 · Cited by 30
Sparse recovery with graph constraints: Fundamental limits and measurement construction
Wang, M., Xu, W., Mallada, E., et al. (2012) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infcom.2012.6195562 · Cited by 30
Consensus in averager-copier-voter networks of moving dynamical agents
Shang, Y. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4976959 · Cited by 29
Scaling Laws for Consensus Protocols Subject to Noise
Jadbabaie, A., & Olshevsky, A. (2018) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2018.2863203 · Cited by 31
Distributed Computing Trade-offs with Random Connectivity
Srinivasavaradhan, S. R., Song, L., & Fragouli, C. (2018) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437653 · Cited by 23
“Therefore, throughout the rest of the work, we impose the connectivity assumption: p ≥ log(K)+Θ(1) K , which guarantees that the random graph is connected with high probability [9].”
Background
Fast Parallel Algorithms for Counting and Listing Triangles in Big Graphs
Arifuzzaman, S., Khan, M., & MARATHE, M. V. (2019) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3365676 · Cited by 30
Delocalization Transition for Critical Erdős–Rényi Graphs
Alt, J., Ducatez, R., & Knowles, A. (2021) · Communications in Mathematical Physics · doi:10.1007/s00220-021-04167-y · Cited by 30
Bernoulli Graph Bounds for Generalrandom Graphs
Butts, C. T. (2011) · Sociological Methodology · doi:10.1111/j.1467-9531.2011.01246.x · Cited by 30
“The power of Theorem 1 (and Corollary 1) lies in the fact that the properties of Bernoulli graphs are much better understood than the properties of general random graphs, the former being the subject of a large and growing portion of the graph theoretic literature (e.g., see Bollob´as 2001).”
Background
Identifying influential spreaders in artificial complex networks
Wang, P., Tian, C., & Lu, J.-A. (2014) · Journal of Systems Science and Complexity · doi:10.1007/s11424-014-2236-4 · Cited by 30
Limited-path-length entanglement percolation in quantum complex networks
Cuquet, M., & Calsamiglia, J. (2011) · Physical Review A · doi:10.1103/physreva.83.032319 · Cited by 27
Managing complexity in industrial collaborations
Schuh, G., Sauer, A., & Doering, S. (2008) · International Journal of Production Research · doi:10.1080/00207540701737781 · Cited by 30
Asymptotic critical transmission ranges for connectivity in wireless ad hoc networks with bernoulli nodes
Wan, P., & Yi, C. (2005) · IEEE Wireless Communications and Networking Conference · doi:10.1109/wcnc.2005.1424861 · Cited by 30
Revealing the microstructure of the giant component in random graph ensembles
Tishby, I., Biham, O., Katzav, E., et al. (2018) · Physical review. E · doi:10.1103/physreve.97.042318 · Cited by 30
COBOUNDARY EXPANDERS
Dotterrer, D., & Kahle, M. (2012) · Journal of Topology and Analysis · doi:10.1142/s1793525312500197 · Cited by 30
Probabilistic heuristics for disseminating information in networks
Stauffer, A. O., & Barbosa, V. C. (2007) · The University of Bath Online Publications Store (The University of Bath) · Cited by 30
Critical epidemics, random graphs, and Brownian motion with a parabolic drift
van der Hofstad, R., Janssen, A. J. E. M., & van Leeuwaarden, J. S. H. (2010) · Advances in Applied Probability · doi:10.1239/aap/1293113157 · Cited by 30
Unstable supercritical discontinuous percolation transitions
Chen, W., Cheng, X., Zheng, Z., et al. (2013) · Physical Review E · doi:10.1103/physreve.88.042152 · Cited by 29
Проблема Эрдеша - Хадвигера и хроматические числа конечных геометрических графов
Raigorodskii, A. M., & Raigorodskii, A. M. (2005) · Математический сборник · doi:10.4213/sm1263 · Cited by 29
On Connectivity and Robustness in Random Intersection Graphs
Zhao, J., Yağan, O., & Gligor, V. (2016) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2016.2601564 · Cited by 29
Weighted Matrix Completion From Non-Random, Non-Uniform Sampling Patterns
Foucart, S., Needell, D., Pathak, R., et al. (2020) · IEEE Transactions on Information Theory · doi:10.1109/tit.2020.3039308 · Cited by 29
Research on a Model of Node and Path Selection for Traffic Network Congestion Evacuation Based on Complex Network Theory
Zhang, G., Jia, H., Yang, L., et al. (2019) · IEEE Access · doi:10.1109/access.2019.2959654 · Cited by 29
Linear stability analysis of large dynamical systems on random directed graphs
Neri, I., & Metz, F. L. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033313 · Cited by 32
The threshold for the square of a Hamilton cycle
Kahn, J., Narayanan, B. P., & Park, J. (2020) · Proceedings of the American Mathematical Society · doi:10.1090/proc/15419 · Cited by 28
An algorithm for counting circuits: Application to real-world and random graphs
Marinari, E., Monasson, R., & Semerjian, G. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10355-0 · Cited by 29
Aligning graphs and finding substructures by a cavity approach
Bradde, S., Braunstein, A., Mahmoudi, H., et al. (2010) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/89/37009 · Cited by 29
On the Connectivity of Sensor Networks Under Random Pairwise Key Predistribution
Yağan, O., & Makowski, A. M. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2265694 · Cited by 29
“Recall that in ER graphs, the property of graph connectivity exhibits the following zero-one law [1]: There is no loss of generality in writing any scaling for the edge assignment probability in the form”
BackgroundMethodInfluential
L -hop percolation on networks with arbitrary degree distributions and its applications
Shang, Y., Luo, W., & Xu, S. (2011) · Physical Review E · doi:10.1103/physreve.84.031113 · Cited by 29
Conflict-Free Colouring of Graphs
Glebov, R., Szabó, T., & Tardos, G. (2013) · Combinatorics Probability Computing · doi:10.1017/s0963548313000540 · Cited by 29
How threshold behaviour affects the use of subgraphs for network comparison
Rito, T., Wang, Z., Deane, C. M., & Reinert, G. (2010) · Bioinformatics · doi:10.1093/bioinformatics/btq386 · Cited by 28
“…should be addressed 1 That is, with Dj(G, H) defined in the main article as being the standardized Euclidean distance between the two scaled and normalized graphlet count vectors the networks G and H for a specific automorphism orbit j, GDDA (geometric mean) = ( 72∏ j=0 ( 1−Dj(G, H) ))1/73 .”
Background
The typical structure of sparse Kr+1-free graphs
Balogh, J., Morris, R., Samotij, W., et al. (2013) · Cited by 29
The Percolation Signature of the Spin Glass Transition
Machta, J., Newman, C. M., & Stein, D. L. (2007) · Journal of Statistical Physics · doi:10.1007/s10955-007-9446-2 · Cited by 29
On the random 2‐stage minimum spanning tree
Flaxman, A. D., FRIEZE, A. M., & Krivelevich, M. (2005) · Random Structures and Algorithms · doi:10.1002/rsa.20079 · Cited by 29
Probabilistic Heuristics for Disseminating Information in Networks
Stauffer, A. O., & Barbosa, V. C. (2007) · IEEE/ACM Transactions on Networking · doi:10.1109/tnet.2007.892877 · Cited by 29
Improving the Gilbert–Varshamov Bound for $q$ -Ary Codes
Vu, V., & Wu, L. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.853300 · Cited by 29

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