10. An Agent-Based Approach to Stability of Complete, Directed, and Signed Social Networks with Loops

An agent-based approach to social networks is developed, and some effects of types of agents to systemic properties of the social networks are clarified. Complete, directed, and signed social networks with loops are investigated, and three types of agents, that is, Heider agents, Newcomb agents, and converse Newcomb agents, are treated. The converse Newcomb agents are newly defined in this work and are proved to have strong effects on self-attitudes, symmetry of attitudes, and stability of the social networks. This work deals with three types of stability, that is, Heider’s stability, Newcomb’s stability, and converse Newcomb stability. The converse Newcomb stability is also newly defined in this work. One of the main propositions establishes the equivalence between Heider’s stability and converse Newcomb stability in complete, directed, and signed social networks with loops. This removes redundancy of the traditional definition of Heider’s stability and refines so-called “Structure Theorem” on Heider’s stability, with respect to complete, directed, and signed social networks with loops.