In this paper, we study `networked bandits', a new bandit problem where a set of interrelated arms varies over time and, given the contextual information that selects one arm, invokes other correlated arms. This problem remains under-investigated, in spite of its applicability to many practical problems. For instance, in social networks, an arm can obtain payoffs from both the selected user and its relations since they often share the content through the network. We examine whether it is possible to obtain multiple payoffs from several correlated arms based on the relationships. In particular, we formalize the networked bandit problem and propose an algorithm that considers not only the selected arm, but also the relationships between arms. Our algorithm is `optimism in face of uncertainty' style, in that it decides an arm depending on integrated confidence sets constructed from historical data. We analyze the performance in simulation experiments and on two real-world offline datasets. The experimental results demonstrate our algorithm's effectiveness in the networked bandit setting.