Year: 2025
Type: preprint
Abstract: Many widely used network centralities are based on counting walks that meet specific criteria. This paper introduces a systematic framework for walk enumeration using generating functions. We introduce a first-passage decomposition that uniquely divides any walk passing through specified nodes or links into two components: a first-reaching walk and a subsequent walk. This decomposition yields a system of interconnected equations that relate three disjoint categories of walks: unrestricted walks, walks that avoid specific elements, and walks that pass through designated sets. The framework offers a range of applications, including evaluating the effects of structural interventions, such as node or link modifications, on network walks, generalizing target centrality to multi-receiver scenarios in information networks, and comparing different strategies for adding links.
Source: arXiv (Cornell University)
Authors: Sun, Yang, Zhao, Wei, Zhou, Junjie
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979381342
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