Mean-field analysis of the convergence time of message-passing computation of harmonic influence in social networks

Abstract

The concept of harmonic influence has been recently proposed as a metric for the importance of nodes in a social network. A distributed message passing algorithm for its computation has been proposed by Vassio et al. (2014) and proved to converge on general graphs by Rossi and Frasca (2016a). In this paper, we want to evaluate the convergence time of this algorithm by using a mean-field approach. The mean-field dynamics is first introduced in a "homogeneous" setting, where it is exact, then heuristically extended to a non-homogeneous setting. The rigorous analysis of the mean-field dynamics is complemented by numerical examples and simulations that demonstrate the validity of the approach.

Effects of Network Communities and Topology Changes in Message-Passing Computation of Harmonic Influence in Social Networks

“…Based on extended simulations on random graphs, the typical convergence time of the algorithm is conjectured to be O(m/n), where m is the number of edges. A mean-field argument by Rossi and Frasca (2017) corroborates this conjecture for homogeneous networks. In general, the limit values overestimate the exact values of the harmonic influence (that is, H (∞) ≥ H( )).…”

On the Convergence of Message Passing Computation of Harmonic Influence in Social Networks

“…This promising insight is confirmed by a mean-field analysis for k-regular graphs, i.e. graphs where every non-field node has the same degree k, where the convergence time depends on k only [31]. Based on these observations, we are lead to conjecture that, at least for a large class of (random) graphs, the typical convergence time of the algorithm be O(m/n), where m is the number of edges.…”