Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The random walk construction of uniform spanning trees and uniform labelled trees
SIAM Journal on Discrete Mathematics
Graph Visualization and Navigation in Information Visualization: A Survey
IEEE Transactions on Visualization and Computer Graphics
Drawing Large Graphs with H3Viewer and Site Manager
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Measurement and analysis of online social networks
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
On the evolution of user interaction in Facebook
Proceedings of the 2nd ACM workshop on Online social networks
What is Twitter, a social network or a news media?
Proceedings of the 19th international conference on World wide web
Visualizing evolving networks: minimum spanning trees versus pathfinder networks
INFOVIS'03 Proceedings of the Ninth annual IEEE conference on Information visualization
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What do large networks look like? Can we visually tell the topological difference between networks such as the Web graph and Facebook network? Due to the huge size of the network, the overall structure will not be discernible if all the nodes and edges are plotted regardless of the graph layout. We reduce the number of nodes and edges by producing a representative subgraph. The nodes are sampled with probability proportional to their degrees, so that large nodes with more connections have a higher probability of being sampled. The edges are reduced further using uniform random spanning tree. The efficacy of the method is demonstrated to preserve the community structure that is characterized by the Network Community Profile (NCP). The result is supported by six real-world large networks, and demonstrated on Twitter user network which contains 4.1 x 107 nodes.