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Theoretical Bounds on the Network Community Profile from Low-rank Semi-definite Programming by Huang, Yufan; Seshadhri, C.; Gleich, David F. is a scholarly article available to read on EtoBox.

What is Theoretical Bounds on the Network Community Profile from Low-rank Semi-definite Programming about?

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.

Author

Huang, Yufan; Seshadhri, C.; Gleich, David F.

Published

2023

Language

EN