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

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.

The manuscript has been substantially shortened from 37 pages to 27 pages. We have extended the analysis to include Spearman's rank correlation coefficients alongside Pearson correlations, which improves the robustness of the comparison, particularly for non-linear relationships and rank-based assessments in heavy-tailed networks. The readability of some figures has been improved