Clustering Vertex-Weighted Graphs by Spectral Methods

Spectral techniques are often used to partition the set of vertices a graph, or form clusters. They based on Laplacian matrix. These allow easily integrate weights edges. In this work, we introduce p-Laplacian, generalized matrix with potential, which also allows us take into account vertices. vertex independent edge weights. way, can cluster importance vertices, assigning more weight some than others, not considering only number We provide bounds, similar those Chegeer, for value minimal cut cost at as function first non-zero eigenvalue p-Laplacian (an analog Fiedler eigenvalue).