Bounded confidence opinion dynamics with network constraints and localized distributed averaging

We study bounded confidence opinion dynamics on graphs. At each iteration, agents average their opinions with those of their neighbors in the graph who have similar opinions. We show that these dynamics converge and study the limiting values. Then we propose and study a variation, called localized distributed averaging, which targets applications where nodes´ opinions or measurements are only useful to other nearby nodes. The utility of localized distributed averaging is illustrated through a source localization example in wireless sensor networks.