  We present the application of topological data analysis (TDA) to study
unweighted complex networks via their persistent homology. By endowing
appropriate weights that capture the inherent topological characteristics of
such a network, we convert an unweighted network into a weighted one. Standard
TDA tools are then used to compute their persistent homology. To this end, we
use two main quantifiers: a local measure based on Forman's discretized version
of Ricci curvature, and a global measure based on edge betweenness centrality.
We have employed these methods to study various model and real-world networks.
Our results show that persistent homology can be used to distinguish between
model and real networks with different topological properties.
