An Algorithm for Generating All Connected Subgraphs with k Vertices of a Graph

In this paper, we introduce a new algorithm ConSubg(k, G) for computing all the connected subgraphs of a fixed size k of a graph G. ConSubg exploits the structure of the graph to prevent the generation of disconnected subgraphs, and is thus particularly advantageous for large sparse graphs. The two main features of our approach are the construction of a combination tree and the definition of an operator ⊗t applied to the nodes of the tree that allow us to generate without duplication the connected subgraphs. We describe and analyze ConSubg(k, G), then demonstrate its effectiveness on random graphs with a fixed degree, scalefree networks, and dual graphs of constraint satisfaction problems.