Network Centrality Metrics Based on Unrestricted Paths, Walks and Cycles Compared to Standard Centrality Metrics

TL;DR

This paper introduces new probabilistic centrality metrics based on unrestricted paths, walks, and cycles, which better capture influence spreading processes compared to traditional shortest-path-based measures.

Contribution

The authors propose novel influence-based centrality metrics that incorporate all feasible paths, walks, and cycles, providing a more comprehensive view of node importance in network flow.

Findings

Betweenness centrality based on influence spreading emphasizes alternative routes.

New metrics show different node rankings compared to standard measures.

Metrics maintain similarity to standard betweenness while highlighting cyclic and recurrent influence.

Abstract

Traditional measures of closeness and betweenness centrality in networks rely on the shortest paths between nodes. Many standard metrics fail to accurately reflect the physical or probabilistic characteristics of nodal centrality and network flow, often overlooking processes such as cyclic and recurrent spreading. Here, we present new metrics based on our influence spreading model. These probabilistic measures consider all feasible paths, walks, and cycles within the network. We define in-centrality to assess how central a node is as a target of influence, and out-centrality for its role as a source of influence. We compare our metrics with standard ones by analyzing node rankings, using scatter plots, and calculating the Pearson correlation and Spearman's rank correlation coefficients. Our findings show that the betweenness centrality defined by the influence spreading model emphasizes the importance of alternative routes while maintaining similarity to standard betweenness centrality.