Abstract

http://ssrn.com/abstract=2150428
 
 

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Tractable and Consistent Random Graph Models


Arun Chandrasekhar


Stanford University - Department of Economics

Matthew O. Jackson


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

September 21, 2012


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 analyze conditions for practical and consistent estimation of the associated network formation parameters, addressing two open issues in the estimation of exponential random graph models. First, there are no previous general results on whether estimates of such a model's parameters based a single network are consistent (i.e., become accurate as the number of nodes grows). Second, a recent literature has shown that standard techniques of estimating ERGMs have exponentially slow mixing times for many specifications in which case the software used for estimating these models will be unreliable. SERGMs reformulate network formation as a distribution over the space of sufficient statistics instead of the space of networks, greatly reducing the size of the space of estimation and making estimation practical and easy. We identify general classes of models for which maximum likelihood estimates are consistent and asymptotically normally distributed. 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 consistent and asymptotically normally distributed. We show how choice-based (strategic) network formation models can be written as SERGMs and SUGMs, and illustrate the application of our models and techniques with network data from villages in Karnataka, India.

Number of Pages in PDF File: 72

Keywords: Random Networks, Random Graphs, Exponential Random Graph Models, Exponential Family, Social Networks, Network Formation, Consistency

JEL Classification: D85, C51, C01, Z13

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Date posted: October 25, 2012 ; Last revised: September 11, 2013

Suggested Citation

Chandrasekhar, Arun and Jackson, Matthew O., Tractable and Consistent Random Graph Models (September 21, 2012). Available at SSRN: http://ssrn.com/abstract=2150428 or http://dx.doi.org/10.2139/ssrn.2150428

Contact Information

Arun Chandrasekhar
Stanford University - Department of Economics ( email )
Stanford, CA 94305
United States
Matthew O. Jackson (Contact Author)
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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