The top figure is a social bipartite network of terrorists with . Nodes' size is proportional to their degree. The two different colors represent the two kinds of vertices. The blue squares stand for people and the red circles represent the organizations. The bottom figure is the coarse-grained network from the BSCG method with . Nodes' size is proportional to its strength in this weighted network.
The evolution of the three largest nontrivial eigenvalues , , and as a function of the size of the coarse-grained network. (a)–(c) The original network is movielens network. (d)–(f) The original network is Netflix network. Red circles correspond to the random coarse graining method, the green line is the community detection method, and the blue squares represent the BSCG method.
Comparison of the MFPT. The walker starts at each node in the top set and the sink i is selected as the node with the strongest weight in the bottom set. The blue circles represent the average MFPT ranked for each group in the original network. The MFPT of the corresponding nodes in the coarse-grained network is displayed with red lines. (a) Nodes merged by BSCG method in Movielens network. (b) Nodes merged randomly in Movielens network. (c) Nodes merged based on community detection method in Movielens network. (d) Nodes merged by BSCG method in Netflix network. (e) Nodes merged randomly in Netflix network. (f) Nodes merged based on community detection method in Netflix network. Insets: Comparison of the exact MFPT between original and the reduced bipartite network. Slope 1 represents the well preserved MFPT in the reduced network.
The three largest nontrivial eigenvalues of in the artificial networks including the bipartite network with community structure and the ER bipartite network. and are the eigenvalues before and after coarse graining, respectively.
The three largest nontrivial eigenvalues of in real-world bipartite networks including a small terrorists' social network, movielens network, and Netflix network. and are, respectively, the eigenvalues before and after coarse graining.
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