  A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network.
Counting of motifs in complex networks has been a well-studied problem in
network analysis of various real-word graphs arising from the study of social
networks and bioinformatics. In particular, the triangle counting problem has
received much attention due to its significance in understanding the behavior
of social networks. Similarly, subgraphs with more than 3 nodes have received
much attention recently. While there have been successful methods developed on
this problem, most of the existing algorithms are not scalable to large
networks with millions of nodes and edges.
  The main contribution of this paper is a preliminary study that genaralizes
the exact counting algorithm provided by Pinar, Seshadhri and Vishal to a
collection of 6-motifs. This method uses the counts of motifs with smaller size
to obtain the counts of 6-motifs with low connecivity, that is, containing a
cut-vertex or a cut-edge. Therefore, it circumvents the combinatorial explosion
that naturally arises when counting subgraphs in large networks.
