Deriving a Nested Chain of Densest Subgraphs from a Graph

A nested chain of densest subgraphs is derived by a computer from a given graph that has multiple vertices and edges. The two ends of each edge are assigned with respective incident weights, and each vertex is given a vertex weight. A weight balancing process is carried out by the computer to iteratively go through the edges to adjust the incident weights of each edge and the vertex weights of the vertices connected by that edge to reduce a difference between the vertex weights of the two vertices. After the balancing, the vertex weights are put in an ordered sequence according to their values, and a nested chain of densest subgraphs is derived from the ordered sequence.