Network Clustering

Clustering can be loosely defined as the process of grouping objects into sets called clusters, so that each cluster consists of elements that are similar in some way. The similarity criterion can be defined in several different ways, depending on applications of interest and the objectives that the clustering aims to achieve. For example, in distance-based clustering (see Figure 1) two or more elements belong to the same cluster if they are close with respect to a given distance metric. On the other hand, in conceptual clustering, which can be traced back to Aristotle and his work on classifying plants and animals, the similarity of elements is based on descriptive concepts. Clustering is used for multiple purposes, including finding “natural” clusters (modules) and describing their properties, classifying the data, and detecting unusual data objects (outliers). In addition, treating a cluster or one of its elements as a single representative unit allows us to achieve data reduction. Network clustering, which is the subject of this chapter, deals with clustering the data represented as a network, or a graph. Indeed, many data types can be conveniently modeled using graphs. This process is sometimes called link analysis. Data points are represented by vertices and an edge exists if two data points are similar or related in a certain way. It is important