Electronic communication service providers are obliged to retain communication data for a certain amount of time by their local laws. The retained communication data or the communication logs are used in various applications such as crime detection, viral marketing, analytical study, and so on. Many of these applications rely on effective techniques for analyzing communication logs. In this paper, we focus on measuring the proximity between two communication entities, which is a fundamental and important step toward further analysis of communication logs, and propose a new proximity measure called ESP (Efficient and Spam-Robust Proximity measure). Our proposed measure considers only the (graph-theoretically) shortest paths between two entities and gives small values to those between spam-like entities and others. Thus, it is not only computationally efficient but also spam-robust. By conducting several experiments on real and synthetic datasets, we show that our proposed proximity measure is more accurate, computationally efficient and spam-robust than the existing measures in most cases.