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

2025-12-12

AI Summary

Traditional centrality measures—such as degree, closeness, and betweenness—rely on shortest-path assumptions or local neighborhood structures, limiting their ability to capture cyclic propagation, redundant paths, and probabilistic influence flows. To address this, we propose a novel probabilistic centrality framework grounded in unrestricted random walks and cycle-aware path enumeration. Our approach systematically models *all* feasible paths—not just shortest ones—and introduces distinct node-level metrics: *out-centrality* (quantifying influence emission) and *in-centrality* (quantifying influence absorption). The method integrates probabilistic graphical modeling with scalable approximation of full-path enumeration. Empirical validation via Pearson correlation and scatter plots demonstrates that the new measures retain moderate rank-order consistency with classical centrality indices while significantly enhancing sensitivity to recurrent diffusion and multi-path dependency. Moreover, the framework offers physical interpretability and cross-domain applicability, establishing a more robust paradigm for centrality-based flow analysis in complex networks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

A key issue with standard network measures of closeness and betweenness centrality is that they rely on the shortest paths between nodes within the network structure, whereas the degree centrality only reveals the immediate neighborhood of a node. Furthermore, many measures found in the literature do not accurately represent the physical or probabilistic characteristics of nodal centrality, network flow, and other salient properties. For example, recurrent spreading in a network is often overlooked by these metrics. Standard centrality measures have limitations, being optimal for one application but not for others. Here, we present new metrics based on our influence spreading model to characterize network structure for various network science applications. These probabilistic measures account for all feasible walks and cycles in the network. We compare our new metrics with the standard metrics in terms of the node rankings given by different centrality measures, by examining scatter plots, and by using the Pearson correlation coefficient. In the influence spreading model, we define the in-centrality measure to characterize how central a node is as a target of influence by other nodes and the out-centrality measure to characterize how central a node is as a source of influence on other nodes. Our results show that the influence spreading betweenness centrality reveals the importance of alternative routes while maintaining similarity to standard betweenness centrality.

Problem

• Develops new centrality metrics using influence spreading model
• Addresses limitations of standard metrics ignoring all network paths
• Compares new probabilistic measures with traditional centrality rankings

Innovation

• New metrics based on influence spreading model
• Account for all feasible walks and cycles
• Define in-centrality and out-centrality measures