k-core decomposition: a tool for the visualization of large scale networks

TL;DR

This paper introduces a scalable visualization method for large networks using k-core decomposition, revealing hierarchical structures efficiently and aiding comparison of different network types.

Contribution

The paper presents a novel, computationally efficient visualization algorithm based on k-core decomposition for large-scale complex networks.

Findings

Effective visualization of large networks highlighting hierarchical cores

Algorithm runs in linear time, suitable for very large sparse networks

Application to real and synthetic graphs demonstrates structural insights

Abstract

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.