Large graph visualization from a hierarchical node clustering

Graphs (or networks) are widely used to model relational data in various application fields (e.g., social network, biological network, Internet network...). Visualization is an important tool to understand the main features of the network but, when the number of nodes in the graph is greater than a few hundreds, standard visualization methods, such as force directed algorithms, are computationally expensive and almost unworkable. Moreover, force directed algorithms do not help the understanding of the structure of the network into dense communities of nodes, which is often a natural way to better understand a network. In this paper, a new visualization method is proposed, based on a hierarchical clustering of the nodes of the graph. This approach can handle the visualization of graphs having several thousands nodes in a few seconds. Several simplified representations of the graph are accessible, giving the user the opportunity to understand the macroscopic organization of the network and then, to focus with more details on some particular parts of the graph. This refining process is controlled by means of Monte Carlo simulation. Partitions under consideration are evaluated via the classical modularity quality measure. A distribution of the quality measure in the case of graphs without structure is obtained by applying the proposed method to random graphs with the same degree distribution as the graph under study. Then only significant partitions (with respect to this random level) are shown during the refining process. This approach is illustrated on several public datasets and compared with other visualization methods meant to emphasize the graph communities. It is also tested on a large network built from a corpus of medieval land charters.