Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given by the fraction of cycles with size four in bipartite networks. Then we compare the two definitions in a special graph, and the results show that the modification one is better to character the network. Next we define a edge-clustering coefficient of bipartite networks to detect the community structure in original bipartite networks.

We introduce a new technique for generating more efficient networks by systematically interlacing bypass rings to torus networks (iBT networks). The resulting network can improve the original torus network by reducing the network diameter, node-to-node distances, and by increasing the bisection width without increasing wiring and other engineering complexity. We present and analyze the statement that a 3D iBT network proposed by our technique outperforms 4D torus networks of the same node degree. We found that interlacing rings of sizes 6 and 12 to all three dimensions of a torus network with meshes 30 Â 30 Â 36 generate the best network of all possible networks, including 4D torus and hypercube of approximately 32,000 nodes. This demonstrates that strategically interlacing bypass rings into a 3D torus network enhances the torus network more effectively than adding a fourth dimension, although we may generalize the claim. We also present a node-to-node distance formula for the iBT networks.

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