Modeling Heterogeneity in Networks using Uncertainty Quantification Tools

TL;DR

This paper introduces a novel method for modeling network heterogeneity by applying Uncertainty Quantification tools, enabling efficient coarse-grained analysis of information propagation dynamics based on node feature distributions.

Contribution

It adapts Polynomial Chaos and Equation-Free methods to quantify and model heterogeneity in network dynamics, providing a new computational framework.

Findings

Efficient coarse-grained representation of network states.

Successful application to information propagation dynamics.

Enhanced understanding of heterogeneity effects on network behavior.

Abstract

Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty Quantification. The crucial assumption underlying this mathematical and computational "technology transfer" is that the evolving states of the nodes in a network quickly become correlated with the corresponding node "identities": features of the nodes imparted by the network structure (e.g. the node degree, the node clustering coefficient). The node dynamics thus depend on heterogeneous (rather than uncertain) parameters, whose distribution over the network results from the network structure. Knowing these distributions allows us to obtain an efficient coarse-grained representation of the network state in terms of the expansion coefficients in suitable orthogonal polynomials. This representation is closely related to mathematical/computational tools for uncertainty quantification (the Polynomial Chaos approach and its associated numerical techniques). The Polynomial Chaos coefficients provide a set of good collective variables for the observation of dynamics on a network, and subsequently, for the implementation of reduced dynamic models of it. We demonstrate this idea by performing coarse-grained computations of the nonlinear dynamics of information propagation on our illustrative network model using the Equation-Free approach