Networks facilitate the exchange of goods and information and create benefits. We consider a network composed of complementary nodes, i.e., nodes that need to be connected to generate a positive payoff. This network may face intelligent attacks on links. To study how the network should be designed, we develop a strategic model, inspired by Dziubiński and Goyal (2013), with two players: a Designer and an Adversary. The Designer has two potential ways to defend her network: forming destructible links among the given set of nodes to increase connectivity or protecting a group of nodes (with indestructible links). Links formation and protections (indestructible links) are costly. The Adversary then allocates her resources to attack links. We examine two situations which differ according to the number of protections available to the Designer. Our main findings are that if the number of protections is not limited, the Designer should either protect all the nodes, or create a large number of (destructible) links to absorb the Adversary's attack; if the available number of protections is limited, then a strategy that uses protections and links can be the equilibrium.