groupsmost

Groupsmost is a term used in network analysis to denote the most cohesive subgroup within a larger network. It refers to a subset of nodes S whose internal connectivity is particularly strong relative to its external connections, according to a chosen cohesion metric.

One common definition for a groupsmost score GMS(S) is GMS(S) = E_in(S) / (E_in(S) + E_out(S)), where E_in(S) counts edges with both ends in S and E_out(S) counts edges that cross from S to the rest of the network. In weighted networks, these counts can be replaced by sums of edge weights. Under this formulation, higher scores indicate a larger share of incident edges that stay inside the group, signaling tighter internal cohesion and comparatively fewer external ties.

Variants exist. A density-based formulation uses GMS_density(S) = E_in(S) / C(|S|, 2), measuring internal density, while conductance-like formulations use ratios that balance internal edges against external exposure. Different studies may normalize by group size or edge weights, leading to multiple practical definitions of the same idea.

Optimization and computation: finding the groupsmost subset S that maximizes GMS(S) is a combinatorial problem and is typically intractable for large networks. Practical approaches rely on heuristics, such as greedy expansion from seed nodes, local search, or spectral and modularity-inspired methods to identify high-scoring subgraphs.

Applications and relation: groupsmost is related to community detection and cohesive subgraph discovery. It is used to identify tight-knit teams, collaboration clusters, or robust cores in various social, biological, and information networks. The exact formulation of groupsmost can vary across studies, reflecting different trade-offs between internal cohesion and external separation.