Asymptotic Results for Configuration Model Random Graphs with Arbitrary Degree Distributions (2010)

09/27/2010 at 10:38 pm

Luke Fostvedt, Dan Nordman, Alyson Wilson

Abstract: We consider a model for generating a random graph using the configuration model. In the configuration model, each node draws a degree independently from a marginal degreed distribution and endpoints pair randomly. We establish non-trivial bounds on the expected sizes of “buckets ” for large graphs. We define nodes i and j in a graph as neighbors if they share an edge, and we define the “bucket ” associated with node i as the set of nodes that are its neighbors and have degree greater than node i. We formalize this argument by providing an analysis for the expected number of items and pairs in a “bucket ” for arbitrarily specified degree distributions, which include power laws.

Paper: Technical Report

JSM 2010: An Example of Performance Analysis for Network Community Detection

08/02/2010 at 9:08 pm

Abstract: Community detection algorithms have many applications ranging from search engines on the world wide web to the detection terrorist networks. While the computer scientists are trying to detect “clumpiness” in networks, as statisticians we are analyzing the performance of the algorithm. We pick a node and determine its expected number of neighbors with a degree greater than or equal to this chosen node. This is colloquially referred to the number of nodes in the chosen node’s “bucket”. We show that, for a multigraph with an arbitrary node degree distribution, both the number of nodes in the bucket and the number of pairs of nodes in the bucket are asymptotically finite. This is in contrast to an Erdos Renyi random graph where this quantity increases with O(n).

Poster: JSM 2010 Poster