Theoretical Bounds on the Network Community Profile from Low-rank Semi-definite Programming
Yufan Huang, C. Seshadhri, David F. Gleich
Abstract
We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of $\mu$-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal $\mu$-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.
BibTeX
@inproceedings{icml2023_theoreticalbound,
title = {Theoretical Bounds on the Network Community Profile from Low-rank Semi-definite Programming},
author = {Yufan Huang and C. Seshadhri and David F. Gleich},
booktitle = {ICML 2023},
year = {2023}
}