Security forces are deployed to protect networks that are threatened by multiple intruders. To select the best deployment strategy, we analyze an interdiction game that considers multiple simultaneous threats. Intruders route through the network as regular customers, while interdictors arrive at specific nodes as negative customers. When an interdictor arrives at a node where an intruder is present, the intruder is removed from the network. Intruders and interdictors compete over the value of this network, which is the throughput of unintercepted intruders. Intruders attempt to maximize this throughput by selecting a fixed route through the network, while the interdictors aim to minimize the throughput selecting their arrival rate at each node. We analyze this game and characterize optimal strategies. For special cases, we obtain explicit formulas to evaluate the optimal strategies and use these to compute optimal strategies for general networks. We also consider the network with probabilistic routing of intruders and show that for this case, the value and optimal strategies of the interdictor of the resulting game remain the same.