On the Convergence Properties of Social Hegselmann–Krause Dynamics

We study the convergence properties of social Hegselmann–Krause (HK) dynamics , a variant HK model opinion dynamics where physical connectivity graph that accounts for extrinsic factors could prevent interaction between certain pairs agents is incorporated. As opposed to original (which terminates in finite time), we show any underlying connected and incomplete graph, under mild assumption, expected termination time social infinity. then investigate rate steady state, provide bounds on maximum $\epsilon$ -convergence terms graph. extend this discussion observe almost all notation="LaTeX">$n$ there exists an -vertex which may not even -converge state within bounded frame. nearly tight necessary sufficient conditions arbitrarily slow merging (a phenomenon essential state). Using conditions, complete notation="LaTeX">$r$ -partite graphs have times.