Discovering dense subgraphs in a graph is a fundamental graph mining task, which has a wide range of applications in social networks, biology and graph visualization to name a few. Even the problems of computing most dense subgraphs (e.g., clique, quasi-clique, k-densest subgraph) are NP-hard, there exists polynomial time algorithms for computing k-core and k-truss. In this paper, we propose a novel dense subgraph, (formula presented), that leverages on a new type of important edges based on the concepts of k-core and k-truss. Compared with k-core and k-truss, (formula presented) can significantly discover the interesting and important structural information outside the scope of the k-core and k-truss. We study two useful problems of (formula presented) decomposition and (formula presented) search. In particular, we develop a (formula presented) decomposition algorithm to find all (formula presented) in a graph G by iteratively removing edges with the smallest (formula presented). In addition, we propose a (formula presented) search algorithm to identify a particular (formula presented) containing a given query node such that the core-number k is the largest. Extensive experiments on several web-scale real-world datasets show the effectiveness and efficiency of the (formula presented) model and proposed algorithms.