jHoles: A Tool for Understanding Biological Complex Networks via Clique Weight Rank Persistent Homology

Abstract

Complex networks equipped with topological data analysis are one of the promising tools in the study of biological systems (e.g. evolution dynamics, brain correlation, breast cancer diagnosis, etc…). In this paper, we propose jHoles, a new version of Holes, an algorithms based on persistent homology for studying the connectivity features of complex networks. jHoles fills the lack of an efficient implementation of the filtering process for clique weight rank homology. We will give a brief overview of Holes, a more detailed description of jHoles algorithm, its implementation and the problem of clique weight rank homology. We present a biological case study showing how the connectivity of epidermal cells changes in response to a tumor presence. The biological network has been derived from the proliferative, differentiated and stratum corneum compartments, and jHoles used for studying variation of the connectivity.