ABSTRACT
Given a set of data points s1, …, sn, we can describes the relationship of the data points by using an undirected graph G = (V,E), where V is the vertex set and E is the edge set. In this article we suppose that the graph is weighted, that is each edge in E carries a non-negative weights wij ≥ 0. The weighted matrix is the similarity matrix W = (wij) i, j = 1, …, n. Since the graph is undirected, the corresponding results are that wij = wji. If wij = 0, this means that the vertexes vi and vj are not connected. The degree of each vertex can be defined as d wi ijj
n . The degree matrix D is defined as the diagonal matrix with the degrees d1, …, dn on the diagonal.
