We introduce and study the Minimum Edge Compact Spanner (MECS) problem on a simple undirected graph. The MECS problem deals with finding a sparse subgraph of an input graph, such that the of average distance or average path length (APL) is preserved to a constant factor. From the perspective of network communication efficiency and robustness, APL can be viewed as a measure of robustness of a communication network in the sense that the shorter the APL, the fewer hops information transmission paths contain on average, thus enhancing robustness of a network with respect to potential transmission errors or disruptions on network links. As a result, such problems have applications in areas where one wants to substitute a dense graph with a sparse subgraph while maintaining a low cost of communication. For example, in the World Wide Web, a short APL enables the rapid transfer of information between websites, thereby reducing communication costs. Similarly, in road networks, a short APL ensures efficient transportation by minimizing the average number of intersections or turns needed to travel between two locations, leading to reduced travel time and fuel consumption. We prove computational complexity results related to the considered problem, design exact and heuristic algorithms for solving the problem, and provide the respective computational results.