Colored Network Motif Analysis by Dynamic Programming Approach: An Application in Host Pathogen Interaction Network

Network motifs are subgraphs of a network which are found with significantly higher frequency than that expected in similar random networks. Motifs are small building blocks of a network and they have emerged as a way to uncover topological properties of complex networks. A special yet not much explored type of motif is the 'colored motif' where color (type) of each node, and hence the edges, in the motif is distinguishable from each other. A traditional motif is defined as a recurring structure in a network, whereas colored motif introduces detailed information about the color of the nodes. G-trie is a data structure to efficiently store a given set of subgraphs by exploiting the topological overlaps within them. In this article we have implemented a modified g-trie to store colored subgraphs and developed a method to discover colored motifs. Our method uses an approximate enumeration for counting the subgraphs to reduce the runtime. We have applied our method to find colored motifs of size three in a host pathogen protein-protein interaction network having two types of proteins namely HIV-1 and human proteins, and four types of edges. Here, we have discovered eight motifs, six of which contain both HIV-1 and human proteins, while the remaining two contain only human proteins.