I. Introduction
Real-life networks, such as social networks, web graphs, and biological networks, often contain frequently-occurring small subgraph structures. Such frequent small subgraphs are referred to as network motifs [1]. Counting the motifs is a fundamental tool in many network analysis applications, including social network analysis, community detection, and bioinformatics [1], [2], [3], [4], [5]. Perhaps the most elementary motif in a graph is the \$k\$-clique which has been widely used in a variety of network analysis applications [1], [2], [6], [7], [8].