Influence and Connectivity in Networks: A Generating Function Approach
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909735707475968 |
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| author | Sun, Yang Zhao, Wei Zhou, Junjie |
| author_facet | Sun, Yang Zhao, Wei Zhou, Junjie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Influence and Connectivity in Networks: A Generating Function Approach Sun, Yang Zhao, Wei Zhou, Junjie Theoretical Economics 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. |
| title | Influence and Connectivity in Networks: A Generating Function Approach |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2508.09492 |