arXiv:1208.2534cs.SI
Locating the Source of Diffusion in Large-Scale Networks
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Abstract
How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^α), where α=1 for arbitrary trees, and α=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades.
The hops were on communities connected by water supplies, not social graphs. In the graph of communities connected by water supplies, 4 hops is relatively short. (See Figure 3b in http://arxiv.org/pdf/1208.2534v1.pdf) Unfortunately, I agree with you that it is difficult to judge…
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