Groupusually

Groupusually is a term in group dynamics and data analysis describing how likely a subset of actors is to stay together across time. It measures the consistency of cohesion under a specified criterion.

Definition: Let V be a population and T a set of time steps. For S ⊆ V and a cohesion predicate Coh(S, t) testing whether S forms a cohesive group at time t, GU(S) is the proportion of times t ∈ T with Coh(S, t) true. If T is finite, GU(S) = (1/|T|) Σ_t 1{Coh(S, t)}; in stochastic settings, GU(S) is the expected value of Coh(S, t).

Properties: GU(S) ranges from 0 to 1. Higher values indicate greater persistence of the group. The measure depends on the chosen cohesion criterion and on time resolution; changing either can alter GU for the same S.

Calculation: Compute GU from a time-ordered sequence of group definitions and a reproducible Coh test. Coh can be based on density, interaction frequency, or another cohesion metric. For probabilistic data, GU is estimated by sampling or simulation.

Applications: Used to assess stability in dynamic clustering, social networks, teams, and collaborations, helping identify groups that are consistently cohesive across contexts.

Limitations: Subject to choices of cohesion metric, time granularity, and sampling. Not a universal standard, so cross-study comparisons require methodological alignment. Related ideas include stability, cohesion, and temporal networks.

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