This article proposes an implicit enumeration approach to solve the maximum ratio (Formula presented.) -plex and the maximum ratio (Formula presented.) -defective clique problems. The approach is inspired by the classical Bron-Kerbosch algorithm for enumerating all maximal cliques in a graph, which is extended to enumerating structures that are hereditary on induced subgraphs. Such structures include (Formula presented.) -plexes and (Formula presented.) -defective cliques, among many others. The performance of the proposed approach is compared with that of the methods based on mixed integer linear programming (MILP), binary search, and Newton's iteration through numerical experiments on randomly generated and real-life network instances.