Abstract
Data based source localization in complex networks has a broad range of applications. Despite recent progress, locating multiple diffusion sources in time varying networks remains to be an outstanding problem. Bridging structural observability and sparse signal reconstruction theories, we develop a general framework to locate diffusion sources in time varying networks based solely on sparse data from a small set of messenger nodes. A general finding is that large degree nodes produce more valuable information than small degree nodes, a result that contrasts that for static networks. Choosing large degree nodes as the messengers, we find that sparse observations from a few such nodes are often sufficient for any number of diffusion sources to be located for a variety of model and empirical networks. Counterintuitively, sources in more rapidly varying networks can be identified more readily with fewer required messenger nodes.
Highlights
Diffusion and propagation processes taking place in complex networks are ubiquitous in natural and in technological systems[1,2], Examples of those processes include air or water pollution diffusion[3,4], disease or epidemic spreading in the human society[5,6], virus invasion in computer and mobile phone networks[7,8], behavior propagation in online social networks[9]
We demonstrate that sparse data from a small set of messenger nodes are capable of identifying multiple diffusion sources accurately and efficiently, even in the absence of detailed information about the network structure such as link weights and the presence of measurement noise
Where xi(t) is the state of node i at time t capturing the fraction of infected individuals, the concentration of water or air pollutant and etc., at place i. β is the constant diffusion coefficient, and wij(t) is the link weight at time t, where self loops are a result of the diffusion process[2]
Summary
Diffusion and propagation processes taking place in complex networks are ubiquitous in natural and in technological systems[1,2], Examples of those processes include air or water pollution diffusion[3,4], disease or epidemic spreading in the human society[5,6], virus invasion in computer and mobile phone networks[7,8], behavior propagation in online social networks[9]. Our knowledge, there has been no solution to the problem of locating multiple diffusion sources associated with general dynamical processes on arbitrary time varying networks from local observations[24].
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