This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, k-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high k-path centrality have high node betweenness centrality. The randomized algorithm runs in time $O(\kappa^{3}n^{2-2\alpha}\log n)$ and outputs, for each vertex v, an estimate of its k-path centrality up to additive error of $\pm n^{1/2+ \alpha}$ with probability $1-1/n^2$. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms.Comment: 16 pages, 10 figures, 2 table

Supplementary data are available at Bioinformatics online.

Online gaming is a multi-billion dollar industry that entertains a large, global population. One unfortunate phenomenon, however, poisons the competition and the fun: cheating. The costs of cheating span from industry-supported expenditures to detect and limit cheating, to victims' monetary losses due to cyber crime.This paper studies cheaters in the Steam Community, an online social network built on top of the world's dominant digital game delivery platform. We collected information about more than 12 million gamers connected in a global social network, of which more than 700 thousand have their profiles flagged as cheaters. We also collected in-game interaction data of over 10 thousand players from a popular multiplayer gaming server. We show that cheaters are well embedded in the social and interaction networks: their network position is largely undistinguishable from that of fair players. We observe that the cheating behavior appears to spread through a social mechanism: the presence and the number of cheater friends of a fair player is correlated with the likelihood of her becoming a cheater in the future. Also, we observe that there is a social penalty involved with being labeled as a cheater: cheaters are likely to switch to more restrictive privacy settings once they are tagged and they lose more friends than fair players. Finally, we observe that the number of cheaters is not correlated with the geographical, real-world population density, or with the local popularity of the Steam Community.This analysis can ultimately inform the design of mechanisms to deal with anti-social behavior (e.g., spamming, automated collection of data) in generic online social networks.