The DOI matches its Crossref record; 281 of the 281 references it cites were found in a registry or an index.
A Survey of Statistical Network Models
Open accessAbstract
Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active “network community” and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online “networking communities” such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Items 201–281 of 281
Respondent‐driven sampling as Markov chain Monte Carlo
Goel, S., & Salganik, M. J. (2009) · Statistics in Medicine · doi:10.1002/sim.3613 · Cited by 203
Nonrespondents in Communication Network Studies: Problems and Possibilities
Stork, D., & Richards, W. D. (1992) · Group & Organization Management · doi:10.1177/1059601192172006 · Cited by 201
Analyzing Social Networks as Stochastic Processes
Wasserman, S. (1980) · Journal of the American Statistical Association · doi:10.1080/01621459.1980.10477465 · Cited by 200
Generalized blockmodeling of two-mode network data
Doreian, P., Batagelj, V., & Ferligoj, A. (2004) · Social Networks · doi:10.1016/j.socnet.2004.01.002 · Cited by 199
Random graph models for temporal processes in social networks
Robins, G., & Pattison, P. (2001) · The Journal of Mathematical Sociology · doi:10.1080/0022250x.2001.9990243 · Cited by 197
p2: a random effects model with covariates for directed graphs
van Duijn, M. A. J., Snijders, T. A. B., & Zijlstra, B. J. H. (2004) · Statistica Neerlandica · doi:10.1046/j.0039-0402.2003.00258.x · Cited by 196
Inferring network mechanisms: The Drosophila melanogaster protein interaction network
Middendorf, M., Ziv, E., & Wiggins, C. H. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0409515102 · Cited by 196
Modeling homophily and stochastic equivalence in symmetric relational data
Hoff, P. D. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0711.1146 · Cited by 194
van Duijn, M. A. J., Gile, K. J., & Handcock, M. S. (2009) · Social Networks · doi:10.1016/j.socnet.2008.10.003 · Cited by 187
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Brandes, U., & Erlebach, T. (2005) · Springer eBooks · Cited by 184
Detecting implausible social network effects in acne, height, and headaches: longitudinal analysis
Cohen-Cole, E., & Fletcher, J. M. (2008) · BMJ · doi:10.1136/bmj.a2533 · Cited by 183
The nature of the social agent*
Carley, K., & Newell, A. (1994) · The Journal of Mathematical Sociology · doi:10.1080/0022250x.1994.9990145 · Cited by 178
The Diameter of a Cycle Plus a Random Matching
Bollobás, B., & Chung, F. R. K. (1988) · SIAM Journal on Discrete Mathematics · doi:10.1137/0401033 · Cited by 176
The link prediction problem for social networks
Liben‐Nowell, D., & Kleinberg, J. M. (2003) · ACM International Conference on Information and Knowledge Management (CIKM) · doi:10.1145/956958.956972 · Cited by 174
Euclidean Embedding of Co-Occurrence Data
Globerson, A., Chechik, G., Pereira, F. M. B., & Tishby, N. (2004) · Cited by 173
Variational Inference for Large-Scale Models of Discrete Choice
Braun, M., & McAuliffe, J. (2010) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.tm08030 · Cited by 169
An assessment of preferential attachment as a mechanism for human sexual network formation
Jones, J. H., & Handcock, M. S. (2003) · Proceedings of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rspb.2003.2369 · Cited by 165
Solution of the two-star model of a network
Park, J., & Newman, M. E. J. (2004) · Physical Review E · doi:10.1103/physreve.70.066146 · Cited by 164
Missing data in networks: exponential random graph (p∗) models for networks with non-respondents
Robins, G., Pattison, P., & Woolcock, J. (2004) · Social Networks · doi:10.1016/j.socnet.2004.05.001 · Cited by 163
Learning Probabilistic Relational Models
Getoor, L. (2000) · Lecture notes in computer science · doi:10.1007/3-540-44914-0_25 · Cited by 152
Latent Space Approaches to Social Network Analysis
Hoff, P. D., Raftery, A. E., & Handcock, M. S. (2001) · doi:10.21236/ada458734 · Cited by 150
Large-scale structure of time evolving citation networks
Leicht, E. A., Clarkson, G., Shedden, K., & Newman, M. E. J. (2007) · The European Physical Journal B · doi:10.1140/epjb/e2007-00271-7 · Cited by 148
Pachinko allocation: dag-structured mixture models of topic correlations
McCallum, A., & Li, W. (2007) · Cited by 143
An experimental study of the small world problem
Travers, J. B., & Milgram, S. (2011) · Princeton University Press eBooks · doi:10.1515/9781400841356.130 · Cited by 142
Smart Agents and Organizations of the Future
Carley, K. M. (2018) · SAGE Publications Ltd eBooks · doi:10.4135/9781848608245.n16 · Cited by 141
Shape and efficiency in spatial distribution networks
Gastner, M. T., & Newman, M. E. J. (2006) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2006/01/p01015 · Cited by 138
A Critical Point for Random Graphs with a Given Degree Sequence
Molloy, M. S. O., & Reed, B. A. (2011) · Princeton University Press eBooks · doi:10.1515/9781400841356.240 · Cited by 136
Stochastic a posteriori blockmodels: Construction and assessment
Wasserman, S. S., & Anderson, C. J. (1987) · Social Networks · doi:10.1016/0378-8733(87)90015-3 · Cited by 127
Simulation for Statistical Inference in Dynamic Network Models
Snijders, T. A. B., & van Duijn, M. A. J. (1997) · Lecture notes in economics and mathematical systems · doi:10.1007/978-3-662-03366-1_38 · Cited by 118
Bibliometric impact measures leveraging topic analysis
Mann, G. S., Mimno, D., & McCallum, A. (2006) · ACM/IEEE-CS Joint Conference on Digital Libraries (JCDL) · doi:10.1145/1141753.1141765 · Cited by 116
Discrete Temporal Models of Social Networks
Hanneke, S., & Xing, E. P. (2008) · Springer eBooks · doi:10.1007/978-3-540-73133-7_9 · Cited by 115
Bayesian inference for dynamic social network data
Koskinen, J. H., & Snijders, T. A. B. (2007) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2007.04.011 · Cited by 113
Weighted graphs and disconnected components
McGlohon, M., Akoglu, L., & Faloutsos, C. (2008) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/1401890.1401955 · Cited by 111
Koskinen, J. H., Robins, G. L., & Pattison, P. E. (2009) · Statistical Methodology · doi:10.1016/j.stamet.2009.09.007 · Cited by 111
Banks, D. L., & Carley, K. M. (1996) · Journal of Mathematical Sociology · doi:10.1080/0022250x.1996.9990179 · Cited by 110
Huss, M., & Holme, P. (2007) · IET Systems Biology · doi:10.1049/iet-syb:20060077 · Cited by 110
Collective classification with relational dependency networks
Neville, J., & Jensen, D. D. (2003) · Cited by 105
Ratmann, O., Jørgensen, O., Hinkley, T., Stumpf, M. P. H., Richardson, S. T., & Wiuf, C. (2005) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030230 · Cited by 102
A Geometric Preferential Attachment Model of Networks
Flaxman, A. D., FRIEZE, A. M., & Vera, J. C. (2006) · Internet Mathematics · doi:10.1080/15427951.2006.10129124 · Cited by 102
Sexual contacts and epidemic thresholds
Jones, J. H., & Handcock, M. S. (2003) · Nature · doi:10.1038/423605a · Cited by 102
Metric inference for social networks
Banks, D. L., & Carley, K. M. (1994) · Journal of Classification · doi:10.1007/bf01201026 · Cited by 98
Morris, M., Handcock, M. S., Miller, W. C., Ford, C. A., Schmitz, J. L., Hobbs, M. M., Cohen, M. S., Harris, K. M., & Udry, J. R. (2006) · American Journal of Public Health · doi:10.2105/ajph.2004.054759 · Cited by 96
Terrorism Informatics: Knowledge Management and Data Mining for Homeland Security
Chen, H., Reid, E. O. F., Sinai, J., Silke, A., & Ganor, B. (2008) · Integrated series on information systems/Integrated series in information systems · doi:10.1007/978-0-387-71613-8 · Cited by 92
Handcock, M. S., Hunter, D. R., Butts, C. T., et al. (2007) · Cited by 92
Learning probabilistic models of link structure
GetoorLisa, FriedmanNir, KollerDaphne, et al. (2003) · Journal of Machine Learning Research · doi:10.5555/944919.944950 · Cited by 88
Models for network dynamics: A Markovian framework
Leenders, R. (1995) · Journal of Mathematical Sociology · doi:10.1080/0022250x.1995.9990149 · Cited by 86
Search Parameters for the Small World Problem
White, H. C. (1970) · Social Forces · doi:10.1093/sf/49.2.259 · Cited by 86
Discovering Hidden Groups in Communication Networks
Baumes, J., Goldberg, M., Magdon‐Ismail, M., et al. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-25952-7_28 · Cited by 86
A Latent Space Approach to Dynamic Embedding of Co-occurrence Data
Sarkar, P., Siddiqi, S. M., & Gordon, G. J. (2007) · Cited by 84
Simple methods for simulating sociomatrices with given marginal totals
Roberts, J. M. (2000) · Social Networks · doi:10.1016/s0378-8733(00)00026-5 · Cited by 82
Network Sampling and Model Fitting
Frank, O. (2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511811395.003 · Cited by 81
Identifying Community Structures from Network Data via Maximum Likelihood Methods
Čopič, J., Jackson, M. O., & Kirman, A. P. (2009) · The B E Journal of Theoretical Economics · doi:10.2202/1935-1704.1523 · Cited by 77
OR FORUM—Catching the “Network Science” Bug: Insight and Opportunity for the Operations Researcher
Alderson, D. (2008) · Operations Research · doi:10.1287/opre.1080.0606 · Cited by 75
Clearing the FOG: Fuzzy, overlapping groups for social networks
Davis, G. B., & Carley, K. M. (2008) · Social Networks · doi:10.1016/j.socnet.2008.03.001 · Cited by 74
Getting Started in Probabilistic Graphical Models
Airoldi, E. M. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030252 · Cited by 72
Self-citationA likelihood approach to analysis of network data
Wiuf, C., Brameier, M., Hagberg, O., & Stumpf, M. P. H. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0600061103 · Cited by 71
Finding Strongly Knit Clusters in Social Networks
Mishra, N., Schreiber, R., Stanton, I., & Tarjan, R. E. (2008) · Internet Mathematics · doi:10.1080/15427951.2008.10129299 · Cited by 69
RTG: a recursive realistic graph generator using random typing
Akoglu, L., & Faloutsos, C. (2009) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-009-0140-7 · Cited by 69
Not Comparable, But Complementary
Jensen, L. J., & Peer Bork, B. (2008) · Science · doi:10.1126/science.1164801 · Cited by 65
An Exponential Family of Probability Distributions for Directed Graphs: Comment
Fienberg, S. E., & Wasserman, S. S. (1981) · Journal of the American Statistical Association · doi:10.2307/2287039 · Cited by 65
Self-citationA stochastic spectral analysis of transcriptional regulatory cascades
Walczak, A. M., Mugler, A., & Wiggins, C. H. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0811999106 · Cited by 61
Statistical Methods for Network Dynamics
Snijders, T. A. B. (2006) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 60
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
Self-citationReid, E. O. F., Qin, J., Chung, W., Xu, J., Zhou, Y., Schumaker, R. P., Sageman, M., & Chen, H. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-25952-7_10 · Cited by 51
RTG: A Recursive Realistic Graph Generator Using Random Typing
Akoglu, L., & Faloutsos, C. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-04180-8_13 · Cited by 48
Tractable learning of large Bayes net structures from sparse data
Goldenberg, A., & Moore, A. (2004) · International Conference on Machine Learning · doi:10.1145/1015330.1015406 · Cited by 47
Self-citationGeneral design principle for scalable neural circuits in a vertebrate retina
Lee, S., & Stevens, C. F. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0705469104 · Cited by 44
Log-normal statistics in e-mail communication patternsPreprint
Stouffer, D. B., Malmgren, R. D., & Amaral, L. A. N. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.physics/0605027 · Cited by 40
From evidence to inference: Probing the evolution of protein interaction networks
Ratmann, O., Wiuf, C., & Pinney, J. W. (2009) · HFSP journal · doi:10.2976/1.3167215 · Cited by 38
Social networks in African elephants
Vance, E. A., Archie, E. A., & Moss, C. J. (2009) · Computational and Mathematical Organization Theory · doi:10.1007/s10588-008-9045-z · Cited by 27
Discovering Functional Communities in Dynamical Networks
Shalizi, C. R., Camperi, M., & Klinkner, K. L. (2008) · Springer eBooks · doi:10.1007/978-3-540-73133-7_11 · Cited by 25
Markov chain Monte Carlo exact inference for social networks
McDonald, J. W., Smith, P. W. F., & Forster, J. J. (2006) · Social Networks · doi:10.1016/j.socnet.2006.04.003 · Cited by 25
An Exponential Family of Probability Distributions for Directed Graphs: Comment
Haberman, S. J. (1981) · Journal of the American Statistical Association · doi:10.2307/2287041 · Cited by 22
Comment on Barabasi, Nature 435, 207 (2005)Preprint
Stouffer, D. B., Malmgren, R. D., & Amaral, L. A. N. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.physics/0510216 · Cited by 21
Transforming Contingency Tables
Meyer, M. M. (1982) · The Annals of Statistics · doi:10.1214/aos/1176345982 · Cited by 20
Learning relational probability trees
Neville, J., Jensen, D. D., Friedland, L., & Hay, M. (2003) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/956804.956830 · Cited by 20
Bayesian mixed-membership models of complex and evolving networks
Fienberg, S. E., Carley, K. M., & Airoldi, E. M. (2006) · Cited by 15
Self-citationMulti-model inference of network properties from incomplete data
Stumpf, M. P. H., & Thorne, T. (2006) · Berichte aus der medizinischen Informatik und Bioinformatik/Journal of integrative bioinformatics · doi:10.1515/jib-2006-32 · Cited by 14
Algebraic Statistics for p 1 Random Graph Models: Markov Bases and Their Uses
Fienberg, S. E., Petrović, S., & Rinaldo, A. (2011) · Lecture notes in statistics · doi:10.1007/978-1-4419-9389-2_2 · Cited by 13
Self-citationMixed membership analysis of high-throughput interaction studies: Relational dataPreprint
Airoldi, E. M., Blei, D. M., Fienberg, S. E., & Xing, E. P. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0706.0294 · Cited by 9
Self-citationExchangeable Random NetworksPreprint
Bassetti, F., Lagomarsino, M. C., & Mandrà, S. (2007) · Cited by 4
Cited by
Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014) · Journal of Complex Networks · doi:10.1093/comnet/cnu016 · Cited by 3,235
Similarity network fusion for aggregating data types on a genomic scale
Wang, B., Mezlini, A. M., Demir, F., Fiume, M., Tu, Z., Brudno, M., Haibe-Kains, B., & Goldenberg, A. (2014) · Nature Methods · doi:10.1038/nmeth.2810 · Cited by 2,036
Self-citationCommunities, modules and large-scale structure in networks
Newman, M. E. J. (2012) · Nature Physics · doi:10.1038/nphys2162 · Cited by 787
A roadmap for the computation of persistent homology
Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017) · EPJ Data Science · doi:10.1140/epjds/s13688-017-0109-5 · Cited by 760
Community Detection and Stochastic Block Models
Abbe, E. (2018) · now publishers, Inc. eBooks · doi:10.1561/9781680834772 · Cited by 544
Metadata
- Authors
- Goldenberg, A., Zheng, A. X., Fienberg, S. E., & Airoldi, E. M.
- Venue
- Foundations and Trends® in Machine Learning
- Publisher
- Emerald
- Published
- 2010-02-16
- Volume
- 2
- Issue
- 2
- Pages
- 129-233
- ISSN
- 1935-8237 (ISSN-L)
- 1935-8245
- OpenAlex
- W2032005951
- Cited by
- 819
- References
- 281
- FWCI
- 28.42
- Type
- journal article
- Language
- en
- Open access
- green
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
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
