Understanding the spreading power of all nodes in a network: a continuous-time perspective

TL;DR

This paper introduces the expected force, a new continuous-time epidemiological metric that accurately measures the spreading power of all nodes in a network, outperforming traditional centrality measures across various network types.

Contribution

The paper proposes the expected force metric, which quantifies node spreading power from a continuous-time perspective, applicable to dynamic and large networks, and demonstrates its effectiveness across different network structures.

Findings

Expected force correlates with node influence more accurately than traditional centralities.

Influence depends on neighbor degree at low power and on own degree at high power.

The metric's effectiveness varies with network density and structure.

Abstract

Centrality measures such as the degree, k-shell, or eigenvalue centrality can identify a network's most influential nodes, but are rarely usefully accurate in quantifying the spreading power of the vast majority of nodes which are not highly influential. The spreading power of all network nodes is better explained by considering, from a continuous-time epidemiological perspective, the distribution of the force of infection each node generates. The resulting metric, the \textit{expected force}, accurately quantifies node spreading power under all primary epidemiological models across a wide range of archetypical human contact networks. When node power is low, influence is a function of neighbor degree. As power increases, a node's own degree becomes more important. The strength of this relationship is modulated by network structure, being more pronounced in narrow, dense networks typical of social networking and weakening in broader, looser association networks such as the Internet. The expected force can be computed independently for individual nodes, making it applicable for networks whose adjacency matrix is dynamic, not well specified, or overwhelmingly large.