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We consider stochastic transition matrices from large social and informationnetworks. For these matrices, we describe and evaluate three fast methods toestimate one column of the matrix exponential. The methods are designed toexploit the properties inherent in social networks, such as a power-law degreedistribution. Using only this property, we prove that one of our algorithms hasa sublinear runtime. We present further experimental evidence showing that allof them run quickly on social networks with billions of edges and accuratelyidentify the largest elements of the column.

Sublinear Column-wise Actions of the Matrix Exponential on Social Networks