Network Clustering by Embedding of Attribute-augmented Graphs

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. The aim is to group vertices which are similar not only in terms of structural connectivity but also in terms of attribute values. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [5, 27]. The augmented graph is embedded in a Euclidean space associated to its Laplacian and apply a modified K-means algorithm to identify clusters. The modified K-means uses a vector distance measure where to each original vertex is assigned a vector-valued set of coordinates depending on both structural connectivity and attribute similarities. To define the coordinate vectors we employ an adaptive AMG (Algebraic MultiGrid) method to identify the coordinate directions in the embedding Euclidean space extending our previous result for graphs without attributes. We demonstrate the effectiveness of our proposed clustering method on both synthetic and real-world attributed graphs.