In this chapter, we explore the use of neighborhood overlap (NOVER), bipartivity index (BPI) and algebraic connectivity (ALGC) as edge centrality metrics to quantify the stability of links for mobile sensor networks. In this pursuit, we employ the notion of the egocentric network of an edge (comprising of the end vertices of the edge and their neighbors as nodes, and the edges incident on the end vertices as links) on which the above three edge centrality metrics are computed. Unlike the existing approach of using the predicted link expiration time (LET), the computations of the above three edge centrality metrics do not require the location and mobility information of the nodes. For various scenarios of node density and mobility, we observe the stability of the network-wide data gathering trees (lifetime) determined using the proposed three edge centrality metrics to be significantly larger than the stability of the LET-based data gathering trees.