The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On inferring autonomous system relationships in the internet
IEEE/ACM Transactions on Networking (TON)
On the origin of power laws in Internet topologies
ACM SIGCOMM Computer Communication Review
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
Power laws and the AS-level internet topology
IEEE/ACM Transactions on Networking (TON)
Simulated Annealing in Convex Bodies and an 0*(n4) Volume Algorithm
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Efficient sampling and feature selection in whole sentence maximum entropy language models
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 01
Microscopic evolution of social networks
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Information Theoretic Comparison of Stochastic Graph Models: Some Experiments
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Evolution of an online social aggregation network: an empirical study
Proceedings of the 9th ACM SIGCOMM conference on Internet measurement conference
A Survey of Statistical Network Models
Foundations and Trends® in Machine Learning
Kronecker Graphs: An Approach to Modeling Networks
The Journal of Machine Learning Research
Measurement-calibrated graph models for social network experiments
Proceedings of the 19th international conference on World wide web
A benchmark diagnostic model generation system
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on model-based diagnostics
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In recent years, there has been a proliferation of theoretical graph models, e.g., preferential attachment and small-world models, motivated by real-world graphs such as the Internet topology. To address the natural question of which model is best for a particular data set, we propose a model selection criterion for graph models. Since each model is in fact a probability distribution over graphs, we suggest using Maximum Likelihood to compare graph models and select their parameters. Interestingly, for the case of graph models, computing likelihoods is a difficult algorithmic task. However, we design and implement MCMC algorithms for computing the maximum likelihood for four popular models: a power-law random graph model, a preferential attachment model, a small-world model, and a uniform random graph model. We hope that this novel use of ML will objectify comparisons between graph models.