Figure 5: Locating an external hidden source from time series.

(a) Hidden source treated as a special node (in red) is connected to four nodes in the network (blue). The time series of other nodes except the source (number 50) after the outbreak of an epidemic are assumed to be available. (b) True adjacency matrix of the NW network with identical link weights to facilitate a comparison with the reconstructed adjacency matrix. (c) Reconstructed adjacency matrix from a number of segments in time series. The four neighbouring nodes of the source are predicted to be densely linked to other nodes, as indicated by the average value of the elements in the four rows corresponding to these nodes. (d) Structural variance σ of each node. The four neighbouring nodes of the source exhibit much larger values of σ than those from the other nodes, providing unequivocal evidence that they belong to the immediate neighbourhood of the hidden source.