On using undirected graph techniques for directed graphs through Category Theory

• DOI: 10.21203/rs.3.rs-1995489/v1
• Publication Date: 2022-08-29T14:45:28Z
• Authors: Sebastian Prado G...; Vivek Kurien George; Vikash Morar; Roldan Joshua; Gabriel Silva
• Keywords: Comparability graph; Modular decomposition; Undirected graph; Graph isomorphism; Cograph; Block graph; Indifference graph; Graph product

Abstract Many complex systems are modeled as graphs. Depending on the setting, graphs can be either directed or undirected. While many computational tools have been developed for both types of graphs, some only exist undirected Thus, creating a ’bridge’ that connects to would unlock potential using graph techniques in appropriate contexts. We used Category Theory novel way map simple bipartite we call prime graph. Formally, show there exists an isomorphism between category and whose objects labeled The labeling is what gives notion direction By taking advantage these two categories, extend contexts by converting into demonstrate this framework applying it problems network alignment spectral clustering.