Abstract
Abstract This paper introduces a concept of an articulation node importance in a multi-robot network, proposes a distributed algorithm to estimate the importance and analyzes a condition to estimate the correct importance value. An articulation node is a weak point of a connected multi-robot network, because the network connectivity will be broken if the robot node is failed. However, the damage to the system when a node failed is depend on a position of the failure node, in other words, a centrality of the node in the network. To evaluate an impact if the node fails, I introduce an definition of the articulation node importance to explain such a centrality. I also introduce an algorithm to estimate the importance in a distributed fashion, and theoretically analyze a condition that the algorithm outputs the correct importance value. How to design a parameter of the algorithm is discussed from results of a numerical example.
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