Interacting Agents in Social Networks: The Idea of Self and Influence Spaces

We study the evolution of social clusters, in an analogy with physical spin systems, and in detail show the importance of the concept of the "self" of each agent with quantifiable variable attributes. We investigate the effective influence space around each agent with respect to each attribute, which allows the cutoff of the Hamiltonian dictating the time evolution and suggest that equations similar to those in general relativity for geodesics in distorted space may be relevant in such a context too. We perform in a simple small-world toy system simulations with weight factors for different couplings between agents and their attributes and spin-type flips in either direction from consideration of a utility function, and observe chaotic, highly aperiodic behavior, with also the possibility of punctuated equilibrium-like phenomena. In a realistic large system, because of the very large number of parameters available, we suggest that it would probably almost always be necessary to reduce the problem to simpler systems with a manageable set of coupling matrices, using assumptions of fuzziness or symmetry or some other consideration.