Title :
Rumors in a Network: Who´s the Culprit?
Author :
Shah, Devavrat ; Zaman, Tauhid
Author_Institution :
Dept. of EECS, Massachusetts Inst. of Technol., Cambridge, MA, USA
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 the popular susceptible-infected (SI) 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 a maximum likelihood (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 nontrivial 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.
Keywords :
graph theory; maximum likelihood detection; maximum likelihood estimation; probability; Internet AS network; US electric power grid network; distance centrality; graph class; maximum likelihood estimator; network centrality notion; network rumors; nontrivial detection probability; rumor centrality; rumor source; rumor spreading; scale-free networks; small-world networks; susceptible-infected model; topological quantity; Computational modeling; Context; Maximum likelihood detection; Maximum likelihood estimation; Probabilistic logic; Silicon; Complex networks; detection algorithms; graph theory; inference algorithms; maximum likelihood (ML) detection; probability;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2158885