The modularity quality function commonly employed for finding community structure in complex networksis generalized in this article to a one-parameter family of quality functions. The generalization of networkmodularity proposed in this work is based on the concept of network efficiency, a metric first proposedby V. Latora and M. Marchiori. We define the efficiency-modularity of a partition based on the differencebetween the actual and expected efficiency among nodes in a community. The one adjustable parameter inefficiency-modularity can be tuned to detect either community or anticommunity structure with a singleunified algorithm.