k_truss(G, k)[source]

Returns the k-truss of G.

The k-truss is the maximal induced subgraph of G which contains at least three vertices where every edge is incident to at least k-2 triangles.

  • G (NetworkX graph) – An undirected graph

  • k (int) – The order of the truss


H – The k-truss subgraph

Return type

NetworkX graph


NetworkXError – The k-truss is not defined for graphs with self loops or parallel edges or directed graphs.


A k-clique is a (k-2)-truss and a k-truss is a (k+1)-core.

Not implemented for digraphs or graphs with parallel edges or self loops.

Graph, node, and edge attributes are copied to the subgraph.

K-trusses were originally defined in [2] which states that the k-truss is the maximal induced subgraph where each edge belongs to at least k-2 triangles. A more recent paper, [1], uses a slightly different definition requiring that each edge belong to at least k triangles. This implementation uses the original definition of k-2 triangles.



Bounds and Algorithms for k-truss. Paul Burkhardt, Vance Faber, David G. Harris, 2018.


Trusses: Cohesive Subgraphs for Social Network Analysis. Jonathan Cohen, 2005.