Fuzzy mixed graphs and its application to identification of COVID19 affected central regions in India

Abstract

In the recent phenomenon of social networks, both online and offline, two nodes may be connected, but they may not follow each other. Thus there are two separate links to be given to capture the notion. Directed links are given if the nodes follow each other, and undirected links represent the regular connections (without following). Thus, this network may have both types of relationships/ links simultaneously. This type of network can be represented by mixed graphs. But, uncertainties in following and connectedness exist in complex systems. To capture the uncertainties, fuzzy mixed graphs are introduced in this article. Some operations, completeness, and regularity and few other properties of fuzzy mixed graphs are explained. Representation of fuzzy mixed graphs as matrix and isomorphism theorems on fuzzy mixed graphs are developed. A network of COVID19 affected areas in India are assumed, and central regions are identified as per the proposed theory.