Title: Malleability of complex networks,
Abstract: Most complex networks are not static, but evolve along time. Given a specific
configuration of one such changing network, it becomes a particularly
interesting issue to quantify the diversity of possible unfoldings of its
topology. In this work, we suggest the concept of malleability of a network,
which is defined as the exponential of the entropy of the probabilities of each
possible unfolding with respect to a given configuration. We calculate the
malleability with respect to specific measurements of the involved topologies.
More specifically, we identify the possible topologies derivable from a given
configuration and calculate some topological measurement of them (e.g.
clustering coefficient, shortest path length, assortativity, etc.), leading to
respective probabilities being associated to each possible measurement value.
Though this approach implies some level of degeneracy in the mapping from
topology to measurement space, it still paves the way to inferring the
malleability of specific network types with respect to given topological
measurements. We report that the malleability, in general, depends on each
specific measurement, with the average shortest path length and degree
assortativity typically leading to large malleability values. The maximum
malleability was observed for the Wikipedia network and the minimum for the
Watts-Strogatz model.