Studies on Neighbourhood Graphs for Communication in Multi Agent Systems
This paper addresses a special type of graph, the k-neighbourhood graph, for the usage in huge multi agent systems. It can be used to establish slim communication structures in extensive groups of agents as they are present e.g. in swarm applications. We will prove some properties of k-neighbourhood graphs in two- and three-dimensional Euclidean space, i.e. we show that the maximum number of incoming connections per agent is limited to a value independent from the overall number of agents in the system. For the two-dimensional case we prove a maximum in-degree of 6 ·k. Furthermore, for agents interacting in three dimensions an upper and a lower bound for this value is presented.
KeywordsSide Length Communication Partner Swarm Intelligence Neighbourhood Graph Incoming Connection
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