Hubsusually

Hubsusually is a term used in network theory to describe nodes that tend to maintain hub status across a broad range of networks and perturbations. It is a coinage intended to signal that hubness can be a robust, typical property rather than an incidental feature of a single network. The term has not achieved wide standardization and appears chiefly in exploratory or method-focused studies.

Definition and interpretation. A node is considered hubsusually if it consistently ranks among the top central nodes (for example, by degree, betweenness, or eigenvector centrality) across an ensemble of networks generated by plausible perturbations such as random edge additions or removals, weight changes, or layer-swapping in multiplex structures. Researchers often contrast hubsusually with context-dependent hubs, which lose hub status under small changes, highlighting a distinction between stable structural roles and transient prominence.

Measurement and methods. A common approach is to compute a centrality measure for each network instance in an ensemble and mark a node as a hub in that instance if it exceeds a chosen threshold (e.g., top k%). The hub persistence index (HPI) can then be defined as the fraction of ensemble networks in which the node is a hub. Additional metrics compare the ranks across networks or aggregate centrality over time in temporal or multilayer networks.

Applications and limitations. Hubsusually is used to identify robust infrastructural or biological core components, informing strategies for resilience, maintenance, and control. Limitations include dependence on the chosen centrality metric, the definition of hub, the size and diversity of the network ensemble, and potential ambiguity in multi-criteria settings. See also hub, centrality, network robustness, and core-periphery.