Tiheiksi

Tiheiksi is a term used in network theory to denote densely connected subgraphs embedded within larger networks. The term, inspired by the Finnish tiheä meaning dense, is used to emphasize structural cohesion rather than narrative or functional boundaries. In many studies, tiheiksi are treated as modular units that facilitate rapid internal interaction while limiting external spillover.

Definition and criteria: A tiheiksi is defined by high internal density and low boundary permeability. Common quantitative criteria include a high clustering coefficient, a high average internal degree relative to the subgraph size, and a density threshold above which a subgraph is considered tiheiksi. Some definitions require short characteristic path lengths between members to ensure fast intra-cluster communication.

Detection and measurement: Tiheiksi can be identified using dense-subgraph algorithms, quasi-clique detection, or k-core decomposition with density constraints. Measures include internal density, average internal degree, and the ratio of internal to external edges. Temporal networks may track tiheiksi as they form, merge, or dissolve.

Applications: In organizational studies, tiheiksi highlight collaboration hubs. In epidemiology, they model rapid spread within tightly connected groups. In online platforms, tiheiksi correspond to tight-knit user groups, such as close circles or interest communities, that shape information diffusion.

Relation to other concepts: Tiheiksi are related to, but distinct from, communities defined by modularity. Critics note overlap with dense communities and warn about sensitivity to network size and sampling. Ongoing work seeks standard definitions and robust detection methods.