A fresh look at network science: Interdependent multigraphs models inspired from statistical physics

Abstract

We consider several challenging problems in complex networks (communication, control, social, economic, biological, hybrid) as problems in cooperative multi-agent systems. We describe a general model for cooperative multi-agent systems that involves several interacting dynamic multigraphs and identify three fundamental research challenges underlying these systems from a network science perspective. We show that the framework of constrained coalitional network games captures in a fundamental way the basic tradeoff of benefits vs. cost of collaboration, in multi-agent systems, and demonstrate that it can explain network formation and the emergence or not of collaboration. Multi-metric problems in such networks are analyzed via a novel multiple partially ordered semirings approach. We investigate the interrelationship between the collaboration and communication multigraphs in cooperative swarms and the role of the communication topology, among the collaborating agents, in improving the performance of distributed task execution. Expander graphs emerge as efficient communication topologies for collaborative control. We relate these models and approaches to statistical physics.