Two-Path Operators, Triadic Decompositions, and Safe Quotients for Ego-Centered Network Compression
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912960081821696 |
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| author | Boudourides, Moses |
| author_facet | Boudourides, Moses |
| contents | Two-paths (wedges) are the elementary combinatorial objects behind clustering, triadic closure, redundancy, and brokerage. Motivated by a two-path formalism that links Burt's structural holes to node-centered ego networks, we develop an operator viewpoint in which wedge incidence induces a canonical ``two-walk'' matrix and a unique decomposition into an edge--supported (triadic) part and a nonedge-supported (open) part. We then study quotient/contraction constructions designed to compress collections of dominating ego networks together with selected ``traversing'' nodes, and we prove a safe (inequality) transfer theorem for two--walk mass under contraction, with an explicit nonnegative error and an equality characterization in terms of a wedge--equitable partition. Finally, we illustrate the theory on ten benchmark graphs and their ego-traversing contractions using table-driven diagnostics and two distribution figures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10258 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-Path Operators, Triadic Decompositions, and Safe Quotients for Ego-Centered Network Compression Boudourides, Moses Social and Information Networks Two-paths (wedges) are the elementary combinatorial objects behind clustering, triadic closure, redundancy, and brokerage. Motivated by a two-path formalism that links Burt's structural holes to node-centered ego networks, we develop an operator viewpoint in which wedge incidence induces a canonical ``two-walk'' matrix and a unique decomposition into an edge--supported (triadic) part and a nonedge-supported (open) part. We then study quotient/contraction constructions designed to compress collections of dominating ego networks together with selected ``traversing'' nodes, and we prove a safe (inequality) transfer theorem for two--walk mass under contraction, with an explicit nonnegative error and an equality characterization in terms of a wedge--equitable partition. Finally, we illustrate the theory on ten benchmark graphs and their ego-traversing contractions using table-driven diagnostics and two distribution figures. |
| title | Two-Path Operators, Triadic Decompositions, and Safe Quotients for Ego-Centered Network Compression |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2603.10258 |