Bursting activity spreading through asymmetric interactions

TL;DR

This paper investigates how the structure and distribution of interactions in social networks influence endogenous bursting activity, revealing critical conditions for activity spikes depending on connection regulation methods.

Contribution

It introduces a multi-dimensional self-exciting process model to analyze the impact of network topology and interaction distribution on bursting activity in social networks.

Findings

Bursting can occur with infinitesimal interaction strength in scale-free networks under input regulation.

Critical interaction strength is approximately 0.3 under output regulation, regardless of degree dispersion.

Stability of human activity depends on both network topology and interaction distribution method.

Abstract

People communicate with those who have the same background or share a common interest by using a social networking service (SNS). News or messages propagate through inhomogeneous connections in an SNS by sharing or facilitating additional comments. Such human activity is known to lead to endogenous bursting in the rate of message occurrences. We analyze a multi-dimensional self-exciting process to reveal dependence of the bursting activity on the topology of connections and the distribution of interaction strength on the connections. We determine the critical conditions for the cases where interaction strength is regulated at either the point of input or output for each person. In the input regulation condition, the network may exhibit bursting with infinitesimal interaction strength, if the dispersion of the degrees diverges as in the scale-free networks. In contrast, in the output regulation condition, the critical value of interaction strength, represented by the average number of events added by a single event, is a constant $1-1/\sqrt{2} \approx 0.3$, independent of the degree dispersion. Thus, the stability in human activity crucially depends on not only the topology of connections but also the manner in which interactions are distributed among the connections.