Network compression by node and edge mergers

We give methods to compress weighted graphs (i.e., networks or BisoNets) into smaller ones. The motivation is that large networks of social, biological, or other relations can be complex to handle and visualize. Using the given methods, nodes and edges of a give graph are grouped to supernodes and superedges, respectively. The interpretation (i.e. decompression) of a compressed graph is that a pair of original nodes is connected by an edge if their supernodes are connected by one, and that the weight of an edge equals the weight of the superedge. The compression problem then consists of choosing supernodes, superedges, and superedge weights so that the approximation error is minimized while the amount of compression is maximized. In this chapter, we describe this task as the 'simple weighted graph compression problem'. We also discuss a much wider class of tasks under the name of 'generalized weighted graph compression problem'. The generalized task extends the optimization to preserve longer-range connectivities between nodes, not just individual edge weights. We study the properties of these problems and outline a range of algorithms to solve them, with different trade-offs between complexity and quality of the result. We evaluate the problems and algorithms experimentally on real networks. The results indicate that weighted graphs can be compressed efficiently with relatively little compression error.