ABSTRACT
We introduce bunch graphs to generalize the structure of graphs, where bunches (groups) are considered essential. The significance of a bunch (a node in a network) is to represent a group as a single entity. We find that simultaneous competition and collaboration are observed among individuals /groups working on a topic/project in the real world. This study captures the notion of simultaneity of competition and collaboration among different species/ communities/ individuals using coopetition bunch graphs. We also introduce two measures for assessing coopetition in a network: a) coopetition number and b) coopetition degree of a node in a bunch graph to capture the competition and collaboration of the node in the network. We identify two types of coopetitions from practice: strong-form coopetition and weak-form coopetition, and corresponding coopetition indices to measure each form of coopetition. We find real-world examples to illustrate our approach and computations for strong-form and weak-form coopetition. The current world is witnessing a global pandemic due to COVID19. The scientists from different research institutes are engaged in overcoming the situation. This study demonstrates that countries and institutes pursue pure competition, collaboration, and coopetition for a variety of reasons (innovation, costs, strategic, and tactical reasons). We compare our approach with that based on existing techniques of semidirected graphs and find that the results of the two approaches are significantly different, largely due to bunch effects. We illustrate this fact at node, sub-graph, and graph levels.