Figure 1
From: Persistent homology of unweighted complex networks via discrete Morse theory
An illustration of the construction of a discrete Morse function f on a clique complex K corresponding to an unweighted and undirected graph G using our algorithm. (a) A simple example of an unweighted and undirected graph G containing 9 vertices and 11 edges. (b) The clique simplicial complex K corresponding to the simple graph G shown in (a). The clique complex K consists of 9 vertices or 0-simplices, 11 edges or 1-simplices and 2 triangles or 2-simplices. The figure also displays the orientation of the 1- and 2-simplices using arrows. (c) Generation of a discrete Morse function f on the clique complex K shown in (b) using our algorithm. The figure lists the state of the Flag variable in algorithm 1 and IsCritical variable in algorithm 2 (See SI Appendix) for each simplex in K. In this example, the clique complex has 4 critical simplices and their respective critical weights correspond to the filtration steps. The figure also lists the FiltrationWeight for each simplex in K obtained using algorithm 3 (See SI Appendix).
