It is well-known that biological and social interaction networks have avarying degree of redundancy, though a consensus of the precise cause of thisis so far lacking. In this paper, we introduce a topological redundancy measurefor labeled directed networks that is formal, computationally efficient andapplicable to a variety of directed networks such as cellular signaling,metabolic and social interaction networks. We demonstrate the computationalefficiency of our measure by computing its value and statistical significanceon a number of biological and social networks with up to several thousands ofnodes and edges. Our results suggest a number of interesting observations: (1)social networks are more redundant that their biological counterparts, (2)transcriptional networks are less redundant than signaling networks, (3) thetopological redundancy of the C. elegans metabolic network is largely due toits inclusion of currency metabolites, and (4) the redundancy of signalingnetworks is highly (negatively) correlated with the monotonicity of theirdynamics.
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