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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 forma...
This paper studies the formation of risk-sharing networks through costly social investments, identifying endogenous inequality and a misallocation of resources as possible downsides to such agreemen...
ESTIMATING AND UNDERSTANDING EXPONENTIAL RANDOM GRAPH MODELS。
In a random graph model based on 3-interactions we give the joint asymptotic distribution of weights and degrees and prove scale-free property for the model. Moreover, we determine the asymptotics of ...
Abstract: We consider the likely size of the endpoint sets produced by Posa rotations, when applied to a longest path in a random graph with $cn,\,c\geq 2.7$ edges that is conditioned to have minimum ...
Abstract: We study the antiferromagnetic Potts model on the Erdos-Renyi random graph. By identifying a suitable interpolation structure and proving an extended variational principle we show that the r...
We introduce a new method for estimating the parameters of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent u...
Consider a critical random multigraph Gn constructed by the con guration model such that its vertex degrees are independent random variables with the same distribution  (criticality means that the se...
Bootstrap percolation on the random graph Gn,p is a process of spread of “activation” on a given realization of the graph with a given number of initially active nodes. At each step those vertices wh...
Holland and Leinhardt (1981) proposed a directed random graph model, the p1 model, to describe dyadic interactions in a social network. In previous work (Petrovic et al., 2010), we studied the algebra...
Vertices of given degree in a random graph
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with...
Component sizes of the random graph outside the scaling window.
We consider the limit distribution of the orders of the k largest components in the Erdös-Rényi random graph inside the ``critical window'' for arbitrary k. We prove a local limit theorem for thi...
We consider the limit distribution of the orders of the k largest components in the Erdös-Rényi random graph inside the ``critical window'' for arbitrary k. We prove a local limit theorem for thi...

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