k-core decomposition: a tool for the visualization of large scale   networks
  We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develop a general visualization algorithm that can be used to compare the structural properties of various networks and highlight their hierarchical structure. The low computational complexity of the algorithm, O(n+e), where 'n' is the size of the network, and 'e' is the number of edges, makes it suitable for the visualization of very large sparse networks. We apply the proposed visualization tool to several real and synthetic graphs, showing its utility in finding specific structural fingerprints of computer generated and real world networks. 
Jos\'e Ignacio Alvarez-Hamelin (LPTO), Luca Dall'Asta (LPTO), Alain   Barrat (LPTO), Alessandro Vespignani (LPTO)