Inter-cluster Transmission Control Using Graph Modal Barriers

TL;DR

This paper introduces a novel method for controlling transmission across graph clusters by assigning barrier weights based on eigenvectors, enabling effective, low-complexity restriction of spread in networks.

Contribution

It proposes a new approach to limit inter-cluster transmission by assigning edge weights derived from Laplacian eigenvectors, avoiding complex graph cuts.

Findings

The method effectively reduces transmission between clusters.

The approach is computationally efficient and suitable for distributed implementation.

Theoretical guarantees support the method's effectiveness.

Abstract

In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus across a computer network, or spread of an infectious disease across communities. The key insight is to assign proper weights to bottleneck edges of the graph based on their role in reducing the connection between two or more strongly-connected clusters within the graph. Selectively reducing the weights (implying reduced transmission rate) on the critical edges helps limit the transmission from one cluster to another. We refer to these as barrier weights and their computation is based on the eigenvectors of the graph Laplacian. Unlike other work on graph partitioning and clustering, we completely circumvent the associated computational complexities by assigning weights to edges instead of performing discrete graph cuts. This allows us to provide strong theoretical results on our proposed methods. We also develop approximations that allow low complexity distributed computation of the barrier weights using only neighborhood communication on the graph.