Approximately Factorizable Networks

Abstract

In factorizable networks, the adjacency (connection strength) between two nodes can be factored into node-specific contributions, named node “conformity”. Often the ith node conformity, CF _i is approximately equal to the scaled connectivity k _i  ∕ sum(k) of the ith node. We describe (a) an algorithm for computing the conformity CF and for measuring the “factorizability” of a general network, and (b) a module- and CF-based decomposition of a general adjacency matrix, which can be used to arrive at a parsimonious description of a network. Approximately factorizable networks have important practical and theoretical applications, e.g., we use them to derive relationships between network concepts. Collaborative work with Jun Dong has shown that network modules (i.e., subnetworks comprised of module nodes) tend to be approximately factorizable (Dong and Horvath BMC Syst Biol 1(1):24, 2007).