The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Small worlds: the dynamics of networks between order and randomness
Small worlds: the dynamics of networks between order and randomness
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Learning Probabilistic Relational Models
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Nexus: Small Worlds and the Groundbreaking Theory of Networks
Nexus: Small Worlds and the Groundbreaking Theory of Networks
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Linked
The Journal of Machine Learning Research
Learning probabilistic models of link structure
The Journal of Machine Learning Research
Learning relational probability trees
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
The link prediction problem for social networks
CIKM '03 Proceedings of the twelfth international conference on Information and knowledge management
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Tractable learning of large Bayes net structures from sparse data
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Generalized Blockmodeling (Structural Analysis in the Social Sciences)
Generalized Blockmodeling (Structural Analysis in the Social Sciences)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Special Issue on Analyzing Large Scale Networks: The Enron Corpus
Computational & Mathematical Organization Theory
ACM SIGKDD Explorations Newsletter
Dynamic social network analysis using latent space models
ACM SIGKDD Explorations Newsletter
Bayes net graphs to understand co-authorship networks?
Proceedings of the 3rd international workshop on Link discovery
A latent mixed membership model for relational data
Proceedings of the 3rd international workshop on Link discovery
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Bibliometric impact measures leveraging topic analysis
Proceedings of the 6th ACM/IEEE-CS joint conference on Digital libraries
Graph model selection using maximum likelihood
ICML '06 Proceedings of the 23rd international conference on Machine learning
Pachinko allocation: DAG-structured mixture models of topic correlations
ICML '06 Proceedings of the 23rd international conference on Machine learning
Group formation in large social networks: membership, growth, and evolution
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Network Visualization by Semantic Substrates
IEEE Transactions on Visualization and Computer Graphics
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics)
Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics)
Mining a digital library for influential authors
Proceedings of the 7th ACM/IEEE-CS joint conference on Digital libraries
Collective entity resolution in relational data
Collective entity resolution in relational data
The phase transition in inhomogeneous random graphs
Random Structures & Algorithms
Bayesian mixed-membership models of complex and evolving networks
Bayesian mixed-membership models of complex and evolving networks
Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning)
Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning)
Euclidean Embedding of Co-occurrence Data
The Journal of Machine Learning Research
Approximate inference, structure learning and feature estimation in markov random fields
Approximate inference, structure learning and feature estimation in markov random fields
An integrated model of traffic, geography and economy in the internet
ACM SIGCOMM Computer Communication Review
Weighted graphs and disconnected components: patterns and a generator
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Mixed Membership Stochastic Blockmodels
The Journal of Machine Learning Research
Mixing Time of Exponential Random Graphs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Terrorism Informatics: Knowledge Management and Data Mining for Homeland Security
Terrorism Informatics: Knowledge Management and Data Mining for Homeland Security
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Dealing with label switching in mixture models under genuine multimodality
Journal of Multivariate Analysis
Social and Economic Networks
Statistical Analysis of Network Data: Methods and Models
Statistical Analysis of Network Data: Methods and Models
RTG: a recursive realistic graph generator using random typing
Data Mining and Knowledge Discovery
Topic and role discovery in social networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Power-Law Distributions in Empirical Data
SIAM Review
Social networks in African elephants
Computational & Mathematical Organization Theory
Counting and locating the solutions of polynomial systems of maximum likelihood equations, I
Journal of Symbolic Computation
Kronecker Graphs: An Approach to Modeling Networks
The Journal of Machine Learning Research
Reconstructing the topology of protein complexes
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Joint group and topic discovery from relations and text
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Statistical models for networks: a brief review of some recent research
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Exploratory study of a new model for evolving networks
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Discrete temporal models of social networks
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Discovering functional communities in dynamical networks
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ISI'05 Proceedings of the 2005 IEEE international conference on Intelligence and Security Informatics
BioWar: scalable agent-based model of bioattacks
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
An introduction to spectral distances in networks
Proceedings of the 2011 conference on Neural Nets WIRN10: Proceedings of the 20th Italian Workshop on Neural Nets
Network sampling and classification: An investigation of network model representations
Decision Support Systems
Generalized latent factor models for social network analysis
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Review of statistical network analysis: models, algorithms, and software
Statistical Analysis and Data Mining
Reachability analysis and modeling of dynamic event networks
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Dynamic stochastic blockmodels: statistical models for time-evolving networks
SBP'13 Proceedings of the 6th international conference on Social Computing, Behavioral-Cultural Modeling and Prediction
Online egocentric models for citation networks
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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.