  This work describes how the formalization of complex network concepts in
terms of discrete mathematics, especially mathematical morphology, allows a
series of generalizations and important results ranging from new measurements
of the network topology to new network growth models. First, the concepts of
node degree and clustering coefficient are extended in order to characterize
not only specific nodes, but any generic subnetwork. Second, the consideration
of distance transform and rings are used to further extend those concepts in
order to obtain a signature, instead of a single scalar measurement, ranging
from the single node to whole graph scales. The enhanced discriminative
potential of such extended measurements is illustrated with respect to the
identification of correspondence between nodes in two complex networks, namely
a protein-protein interaction network and a perturbed version of it. The use of
other measurements derived from mathematical morphology are also suggested as a
means to characterize complex networks connectivity in a more comprehensive
fashion.
