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In the present paper, we derive an upper bound of the average networkbreakdown probability of packet networks with unreliable relay nodes. We hereassume that relay nodes get independently broken with a given node breakdownprobability. A survivor graph is the induced subgraph obtained by removing thebroken relay nodes and their connecting edges from the original graph. If thesurvivor network is disconnected, we consider a network breakdown happens. Theprimal contribution of the paper is to derive an upper bound of the averagenetwork breakdown probability, where the expectation is taken over a regulargraph ensemble. The proof of the bound is based on a natural one-to-onecorrespondence between a regular graph and a regular bipartite graph, and alsoon enumeration of bipartite graphs satisfying certain conditions. This proofargument is inspired by the analysis of weight distribution for low-densityparity-check codes. Compared with estimates of the average network breakdownprobability obtained by computer experiments, it is observed that the upperbound provides the values which are not only upper bounds but also preciseestimates of the network breakdown probability when the node breakdownprobability is small.

Analysis of Breakdown Probability of Wireless Sensor Networks with Unreliable Relay Nodes