  Long lived topological features are distinguished from short lived ones
(considered as topological noise) in simplicial complexes constructed from
complex networks. A new topological invariant, persistent homology, is
determined and presented as a parametrized version of a Betti number. Complex
networks with distinct degree distributions exhibit distinct persistent
topological features. Persistent toplogical attributes, shown to be related to
robust quality of networks, also reflect defficiency in certain connectivity
properites of networks. Random networks, networks with exponential conectivity
distribution and scale-free networks were considered for homological
persistency analysis.
