Tractable and Consistent Random Graph Models

62 Pages Posted: 8 Jul 2014

See all articles by Arun G. Chandrasekhar

Arun G. Chandrasekhar

Stanford University - Department of Economics

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)

Multiple version iconThere are 2 versions of this paper

Date Written: July 2014

Abstract

We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these models' (including ERGMs) parameters estimated from the observation of a single network are consistent (i.e., become accurate as the number of nodes grows). Next, addressing the problem that standard techniques of estimating ERGMs have been shown to have exponentially slow mixing times for many specifications, we show that by reformulating network formation as a distribution over the space of sufficient statistics instead of the space of networks, the size of the space of estimation can be greatly reduced, making estimation practical and easy. We also develop a related, but distinct, class of models that we call subgraph generation models (SUGMs) that are useful for modeling sparse networks and whose parameter estimates are also directly and easily estimable, consistent, and asymptotically normally distributed. Finally, we show how choice-based (strategic) network formation models can be written as SERGMs and SUGMs, and apply our models and techniques to network data from rural Indian villages.

Suggested Citation

Chandrasekhar, Arun G. and Jackson, Matthew O., Tractable and Consistent Random Graph Models (July 2014). NBER Working Paper No. w20276. Available at SSRN: https://ssrn.com/abstract=2463391

Arun G. Chandrasekhar (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

Matthew O. Jackson

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Canadian Institute for Advanced Research (CIFAR) ( email )

180 Dundas Street West, Suite 1400
Toronto, Ontario
Canada

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