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We consider the problem of finding the maximally influential node in random networks where each node influences every other node with constant yet unknown probability. We develop an online algorithm that learns the relative influences of the nodes. It relaxes the assumption in the existing literature that a central observer can monitor the influence spread globally. The proposed algorithm delegates the online updates to the nodes on the network; hence requires only local observations at the nodes. We show that using an explore-then-commit learning strategy, the cumulative regret accumulated by the algorithm over horizon T approaches O(T2/3) for a network with a large number of nodes. Additionally, we show that, for fixed T, the worst case-regret grows linearly with the number n of nodes in the graph. Numerical experiments illustrate this linear dependence for Chung-Lu models. The experiments also demonstrate that ε-greedy learning strategies can achieve similar performance to the explore-then-commit strategy on Chung-Lu models.