Modeling ad hoc sensor networks using random graph theory

Modeling of ad hoc sensor networks becomes difficult when uncertain features of the network increase. Deterministic modeling is difficult and some stochastic arguments should be introduced instead. In this paper, we introduce the concept of random networks. One remarkable feature of random graphs is that a phase transition occurs as the probability of edge connection increases. At the critical probability, fragmented pieces of edges suddenly start to be mutually connected, forming one large component. This graph-theoretical change parallels phase transitions in states of mutter, e.g. the jump from water to ice. In ad hoc sensor networks, the nodes are connected by wireless links. In order to meet this requirement, we propose a model using percolation, a kind of random graph where the edges are formed only between the nearby nodes. We also present some numerical examples to simulate the jump effects of the phase transition.