Large highly connected clusters in protein-protein interaction networks

Abstract

The edge (vertex) connectivity of a graph is the minimum number of edges (vertices) that must be removed to disconnect the graph. Connectivity is an important property of a graph but has seldom been used in the study of protein-protein interaction (PPI) and other biological networks. Connectivity differs from edge density in that it is based on the number of paths between all vertices in the graph, while edge density is based solely on the number of edges. Connectivity may be a better indicator of large clusters than edge density: in real-world networks, as the number of vertices in a cluster increases, the edge density tends to decrease rapidly, but the connectivity tends to remain constant.We developed algorithms to search for subgraphs with high connectivities, proved their correctness and complexity, and applied these algorithms to Saccharomyces cerevisiae and human PPI networks. We discovered that PPI networks have large subgraphs (20-130 vertices) with high connectivity that were previously unrecognized. The function of these subgraphs remains unknown, but they are far more highly connected than subgraphs in random networks and are significantly enriched with proteins with shared biological functions, suggesting that these are biologically significant.