highercore
Highercore is a generalization of the core decomposition concept in graph theory, used in network science to identify robust substructures in multilayer or time-evolving networks. It extends the classic k-core by requiring connectivity thresholds to hold simultaneously across multiple layers or time steps. In a single-layer graph, the highercore reduces to the standard k-core when the threshold vector has a single component.
Consider a multilayer network with vertex set V and layers L1, ..., Lm. Each layer i defines a
Variants may replace degree with other measures, such as strength in weighted networks, or use adaptive thresholds.
Computationally, highercores are typically computed by iterative pruning across layers: initialize with all vertices, remove any
Applications include identifying resilient cores in social, transportation, and biological networks, analyzing multilayer collaborations, and studying
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