Rumors in a Network: Who's the Culprit?

Abstract

We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with a variant of the popular SIR model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term rumor centrality. We establish that this is an ML estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has non-trivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree-like. arXiv:0909.4370v2 [stat.ML]

Trends Prediction Using Social Diffusion Models

“…Kempe et al applied theoretical analysis on the seeds selection problem [9] based on two simple adoption models: Linear Threshold Model and Independent Cascade Model. Recently, Zaman et al developed a method to trace rumors back in the topological spreading path to identify sources in a social network [10], and suggest that methods can be used to locate influencers in a network. Some scholars express their doubts and concerns for the influencer-driven viral marketing approach, suggesting that "everyone is an influencer" [11], and companies "should not rely on it" [12].…”

Morphological inversion of complex diffusion

“…However, this is only feasible for small networks. Message-passing algorithms can approximate the marginals efficiently [12,[14][15][16], however these algorithms are model specific: for every M , one must invent new approximations, heuristic assumptions and analytic calculations.In contrast, the second class of methods works independent of the forward model [14,[17][18][19]. These presuppose that s should be approximately equidistant to all other nodes in C, and therefore, nodes with high "centrality" values should have a higher likelihood of being s. This assumption breaks down if the spread reaches "boundaries", or if the spread self-interacts (i.e.…”

“…While the generation of morphological stencils requires knowing the dynamic law as well as the states of all nodes at some final time, our approach works for all models. In contrast, other inversion schemes are model-specific [12,16,19,20]. Even though our inversion scheme works for any model, it is not model invariant like the centrality based methods which uses only topological properties in the graph.…”

“…Presently, there are two approaches to identify s. The first uses probability marginals from Bayesian methods [12][13][14][15][16][17][18][19][20][21]. In some cases, it is possible to sample the state space using Monte Carlo simulations [13].…”

“…In contrast, the second class of methods works independent of the forward model [14,[17][18][19]. These presuppose that s should be approximately equidistant to all other nodes in C, and therefore, nodes with high "centrality" values should have a higher likelihood of being s. This assumption breaks down if the spread reaches "boundaries", or if the spread self-interacts (i.e.…”