A Fast Counting Method for 6motifs with Low Connectivity A kmotif (or graphlet) is a subgraph on k nodes in a graph or network. Counting of motifs in complex networks has been a wellstudied problem in network analysis of various realword 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.  :102,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 6motifs. This method uses the counts of motifs with smaller size to obtain the counts of 6motifs with low connecivity, that is, containing a cutvertex or a cutedge. Therefore, it circumvents the combinatorial explosion that naturally arises when counting subgraphs in large networks.

Distributed Triangle Counting Algorithms in Simple Graph Stream Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, onepass streaming algorithm for counting global and local triangles has been widely studied, and most researches focus on the singlemachine streaming algorithm in a u0027offlinebatch processingu0027 mode. However, researches on distributed online algorithm on multiple machines are still in its infancy, and this stage has not been thoroughly studied. In this paper, we investigate the triangle counting problem in largescale simple undirected graphs whose edges arrive as a stream. We propose two distributed online streaming algorithms to estimate the global number of triangles, which are based on the current best performance samplingbased streaming algorithm. We mainly realize the reasonable partition of the graph stream, so that each worker independently estimates the number of triangles in a subgraph of the graph stream. Experimental results show that our algorithms reduce the estimation error and are several times more accurate than stateoftheart streaming algorithms.