Top Persuader Prediction for Social Networks

Our proof is built on Perron-Frobenius theorem, a seminal work in matrix theory (Meyer 2000). By Perron-Frobenius theorem, the power iteration algorithm for predicting top K persuaders converges to a unique C and this convergence is independent of the initialization of C if the persuasion probability matrix P is nonnegative, irreducible, and aperiodic (Heath 2002). We first show that P is nonnegative. Each component of the right hand side of Equation (10) is positive except nD $ 0; thus, persuasion probability pij estimated with Equation (10) is positive, for all i, j = 1, 2, ..., n and i ... j. Because all diagonal elements of P are equal to zero and all non-diagonal elements of P are positive persuasion probabilities, P is nonnegative.