Accession Number:

AD1011061

Title:

Capturing the Interplay of Dynamics and Networks through Parameterizations of Laplacian Operators

Descriptive Note:

Journal Article

Corporate Author:

Indiana University Bloomington United States

Report Date:

2016-08-24

Pagination or Media Count:

40.0

Abstract:

We study the interplay between a dynamical process and the structure of the network on which it unfolds using the parameterized Laplacian framework. This framework allows for defining and characterizing an ensemble of dynamical processes on a network beyond what the traditional Laplacian is capable of modeling. This, in turn, allows for studying the impact of the interaction between dynamics and network topology on the quality-measure of network clusters and centrality, in order to effectively identify important vertices and communities in the network. Specifically, for each dynamical process in this framework, we define a centrality measure that captures a vertexs participation in the dynamical process on a given network and also define a function that measures the quality of every subset of vertices as a potential cluster or community with respect to this process. We show that the subset-quality function generalizes the traditional conductance measure for graph partitioning. We partially justify our choice of the quality function by showing that the classic Cheegers inequality, which relates the conductance of the best cluster in a network with a spectral quantity of its Laplacian matrix, can be extended to the parameterized Laplacian. The parameterized Laplacian framework brings under the same umbrella a surprising variety of dynamical processes and allows us to systematically compare the different perspectives they create on network structure.

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE