  It is well-known that biological and social interaction networks have a
varying degree of redundancy, though a consensus of the precise cause of this
is so far lacking. In this paper, we introduce a topological redundancy measure
for labeled directed networks that is formal, computationally efficient and
applicable to a variety of directed networks such as cellular signaling,
metabolic and social interaction networks. We demonstrate the computational
efficiency of our measure by computing its value and statistical significance
on a number of biological and social networks with up to several thousands of
nodes 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) the
topological redundancy of the C. elegans metabolic network is largely due to
its inclusion of currency metabolites, and (4) the redundancy of signaling
networks is highly (negatively) correlated with the monotonicity of their
dynamics.
