Network Alignment (NA) is a generalization of the graph iso-morphism problem for non-isomorphic graphs, where the goal is to find a node mapping as close as possible to isomor-phism. Recent successful NA algorithms follow a search-based approach, such as simulated annealing. We propose to speed up search-based NA algorithms by pruning the search-space based on heuristic rules derived from the topological features of the aligned nodes. We define several desirable properties of such pruning rules, analyze them theoretically, and propose a pruning rule based on nodes' degrees. Experi-mental results show that using the proposed rule yields sig-nificant speedup and higher alignment quality compared to the state of the art. In addition, we redefine common NA ob-jective functions in terms of established statistical analysis metrics, opening a wide range of possible objective functions.