Multiple propagation paths enhance locating the source of diffusion in complex networks

Abstract

We investigate the problem of locating the source of diffusion in complex networks without complete knowledge of nodes' states. Some currently known methods assume the information travels via a single, shortest path, which by assumption is the fastest way. We show that such a method leads to the overestimation of propagation time for synthetic and real networks, where multiple shortest paths as well as longer paths between vertices exist. We propose a new method of source estimation based on maximum likelihood principle, that takes into account existence multiple shortest paths. It shows up to 1.6 times higher accuracy in synthetic and real networks. * lukaszgajewski@tuta.io

Comparison of observer based methods for source localisation in complex networks

“…Four observer placement strategies are evaluated—Betweenness Centrality (BC) 52 that places observers at the nodes with the highest betweenness centrality, High Coverage Rate (HCR) 10 that maximises the number of neighbourhoods to which the observers belong, High Variance Observers (HVO) 49 which maximises the cardinality of the set of nodes lying on the shortest paths between observers, and simply random (RND) as a null model. For location methods, we chose the methods introduced by Pinto et al (LPTV) 1 that maximises likelihood estimator using a breadth-first search tree approximation, by Shen et al (TRBS) 2 that uses a so-called backwards spreading from observers onto the graph, by Xu et al (PC) 5 that relies on the correlation between the topological distance and time of propagation from the source, by Paluch et al (GMLA) 3 that modifies the LPTV by introducing a special node selection method, and by Gajewski et al (EPL) 4 that also modifies the LPTV to account for loops in the graph. Instead of showing the results as the function of the observer budget, K , we chose the observer density in our plots to easily compare systems of different sizes.…”

“…It assumes the normal distribution to calculate expected variances, which is not consistent with actual delay distributions of Susceptible-Infected processes that have geometric distribution. Multiple parallel paths affect not only variances and covariances of the expected times to arrive at observers starting from a specific potential source, but also their mean values 4 . While the distribution assumptions are mismatched, the inclusion of parallel paths allows this method to best predict the actual characteristics of the spreading process and pinpoint the source with the best accuracy.…”

“…As shown by Gajewski et al 4 the assumption of a tree-like propagation is not always satisfied. Treating paths as random variables makes the actual expected time of traversal equal to the first moment of a minimum distribution of all paths connecting two nodes.…”

“…Similarly, covariances between observers become covariances of multivariate minimum distribution. Since establishing general expression for such minimum distribution of an ensemble of n paths is a non-trivial task 55 , even with an identically and independently distributed random variables approximation 4 , one can settle for a known analytical formula in the case of discussed by Nadarajah and Kotz 56 :…”

Countering misinformation: A multidisciplinary approach

“…It is, however, computationally expensive and approximates a tree network which leads to discrepancies for networks with a local structure. These drawbacks have been alleviated by optimized methods that are much faster, or those that take full network structure into account, offering improved accuracy at a higher computational cost (Gajewski et al., 2019; Paluch et al., 2018). Other methods seek to reduce the assumptions required about the spreading process, either by estimating the time distribution from the data or by considering local correlation of arrival times and distances (She et al., 2016; Wang and Sun, 2020).…”