Security games model the confrontation between a defender protecting a set of targets and an attacker who tries to capture them. A variant of these games assumes security interdependence between targets, facilitating contagion of an attack. So far only stochastic spread of an attack has been considered. In this work, we introduce a version of security games, where the attacker strategically drives the entire spread of attack and where interconnections between nodes affect their susceptibility to be captured. We find that the strategies effective in the settings without contagion or with stochastic contagion are no longer feasible when spread of attack is strategic. While in the former settings it was possible to efficiently find optimal strategies of the attacker, doing so in the latter setting turns out to be an NP-complete problem for an arbitrary network. However, for some simpler network structures, such as cliques, stars, and trees, we show that it is possible to efficiently find optimal strategies of both players. For arbitrary networks, we study and compare the efficiency of various heuristic strategies. As opposed to previous works with no or stochastic contagion, we find that centrality-based defense is often effective when spread of attack is strategic, particularly for centrality measures based on the Shapley value.