# Triangle k Core

### From visone user support

The triangle k core, or k truss has been intoduced by Cohen (NSA Tech. Report 2008) and Zhang and Parthasarathy (ICDE 2012) independently and runs in time, where Δ(*G*) is the maximum degree and *m* the number of edges.

### Definition Triangle Core

The triangle k-core of a simple undirected graph *G* = (*V*,*E*) is the inclusion maximal subgraph where each edge is part of at least *k* triangles in *C*_{k}(*G*).

More detailed background information is provided in

- Cohen, Jonathan. "Trusses: Cohesive subgraphs for social network analysis." National Security Agency Technical Report (2008).
- Zhang, Yang, and Srinivasan Parthasarathy. "Extracting analyzing and visualizing triangle k-core motifs within networks." In Data Engineering (ICDE), 2012 IEEE 28th International Conference on, pp. 1049-1060. IEEE, 2012.

### Definition Triangle Core Number

The triangle core number of an edge is the maximal k such that