Understanding how both the partitions of a bipartite network affect its one-mode projection |
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Authors: | Animesh Mukherjee Monojit ChoudhuryNiloy Ganguly |
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Institution: | a Institute for Scientific Interchange (ISI), Viale Settimio Severo 65, 10133 Torino, Italyb Microsoft Research India, Bangalore, 560080, Indiac Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, 721302, India |
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Abstract: | It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations. |
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Keywords: | Bipartite network One-mode projection Discrete combinatorial systems Generating function Convolution |
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