We propose and study a model of strategic network exploration where the hider, subject to a budget constraint restricting the number of links, chooses a connected network and a location of an object. The seeker, who does not observe the network and location of the target chooses a network exploration strategy starting at a fixed node in the network. We obtain a Nash equilibrium and characterize equilibrium payoffs in the case of linking budget allowing for trees only. We also give bounds on the expected number of steps needed find the hider for the case where the linking budget allows for at most one cycle in the network.