Given a network G, edge centrality is a metric used to evaluate the importance of edges in G, which is a key concept in analyzing networks and finds vast applications involving edge ranking. In spite of a wealth of research on devising edge centrality measures, they incur either prohibitively high computation costs or varied deficiencies that lead to sub-optimal ranking quality. To overcome their limitations, this paper proposes ECHO, a new centrality measure for edge ranking that is formulated based on neighborhood-based optimization objectives. We provide in-depth theoretical analyses to unveil the mathematical definitions and intuitive interpretations of the proposed ECHO measure from diverse aspects. Based thereon, we present three linear-complexity algorithms for ECHO estimation with non-trivial theoretical accuracy guarantees for centrality values. Extensive experiments comparing ECHO against six existing edge centrality metrics in graph analytics tasks on real networks showcase that ECHO offers superior practical effectiveness while offering high computation efficiency.