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Deliverable D2.2.4 Statistical properties of directed ad-hoc networks arising from random distributed transmitting powers of agents

In this deliverable we report the analysis made on the problem of networking of mobile agents with random emitting power. This report consists essentially of two contributions (DELIS-TR-0410 and DELIS-TR-0484). The former is a very simplified statistical model that wants to reproduce an elementary process of dynamics in a scale-free network. The main result is that scale invariance is a natural consequence of a suitably chosen extremal dynamics. In the second contribution we consider a more realistic multi-hop ad-hoc network (defined as an undirected network by considering two nodes as adjacent whenever their effective transmitting areas overlap). We show with simple probabilistic reasonings that a so constructed network is minimally connected if the effective transmitting area scales as log N−log log N N with the number N of nodes, irrespective of the area shape.