The Interconnectedness Coefficient: A Semi-Local Graph-Theoretic Measure for Connector Vertices between Cohesive Network Regions
Abstract
The Interconnectedness Coefficient (IC) is a bounded semi-local graph-theoretic node measure designed to identify connector vertices between cohesive network regions. Such connector vertices, also referred to as bridging nodes, may mediate between locally cohesive regions even when they are neither hubs nor themselves highly clustered. The IC preferentially assigns high values to weakly clustered focal vertices whose adjacent vertices remain strongly clustered after exclusion of the focal connection. Candidate vertices are required to have degree at least two. The construction is partition-free, uses information within radius two, and requires no predefined community or module partition. The range and extremal properties of the score are derived analytically. Exact graph families isolate its maximal response to fully cohesive branches, its controlled response to a single cohesion defect, its invariance under a cohesion-free hub extension, and a sharp fragmentation threshold. A separate application to a Human Interactome Map reveals pronounced degree-dependent stabilization of IC values near the network's mean clustering level. This behavior follows directly from the multiplicative definition. If focal clustering tends to zero while mean leave-one-out cohesion in the neighborhood stabilizes, the IC converges to that neighborhood-cohesion level. Among the highly ranked IC vertices are proteins with established interface, scaffold, and adaptor roles in molecular complexes. The IC is therefore positioned as a semi-local connector measure for cohesive network regions.
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BibTeX
@misc{wiebringhaus2026interconnectedness,
title = {{The Interconnectedness Coefficient: A Semi-Local Graph-Theoretic Measure for Connector Vertices between Cohesive Network Regions}},
author = {Thomas Wiebringhaus},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13928},
eprint = {2609.13928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13928},
}
RIS
TY - UNPB
TI - The Interconnectedness Coefficient: A Semi-Local Graph-Theoretic Measure for Connector Vertices between Cohesive Network Regions
AU - Thomas Wiebringhaus
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13928
UR - https://arxiv.org/abs/2609.13928
AB - The Interconnectedness Coefficient (IC) is a bounded semi-local graph-theoretic node measure designed to identify connector vertices between cohesive network regions. Such connector vertices, also referred to as bridging nodes, may mediate between locally cohesive regions even when they are neither hubs nor themselves highly clustered. The IC preferentially assigns high values to weakly clustered focal vertices whose adjacent vertices remain strongly clustered after exclusion of the focal connection. Candidate vertices are required to have degree at least two. The construction is partition-free, uses information within radius two, and requires no predefined community or module partition. The range and extremal properties of the score are derived analytically. Exact graph families isolate its maximal response to fully cohesive branches, its controlled response to a single cohesion defect, its invariance under a cohesion-free hub extension, and a sharp fragmentation threshold. A separate application to a Human Interactome Map reveals pronounced degree-dependent stabilization of IC values near the network's mean clustering level. This behavior follows directly from the multiplicative definition. If focal clustering tends to zero while mean leave-one-out cohesion in the neighborhood stabilizes, the IC converges to that neighborhood-cohesion level. Among the highly ranked IC vertices are proteins with established interface, scaffold, and adaptor roles in molecular complexes. The IC is therefore positioned as a semi-local connector measure for cohesive network regions.
ER -