On the degree distribution of projected networks mapped from bipartite networks |
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| Authors: | JC Nacher T Akutsu |
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| Institution: | 1. Department of Complex and Intelligent Systems, Future University Hakodate, Hakodate, 041-8655, Hokkaido, Japan;2. Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, 611-0011, Japan;1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;2. AVIC Aeroengine Control Research Institute, Wuxi 214063, China;1. Instituto de Cálculo UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Int. Guiraldes 2160, (1428) Buenos Aires, Argentina;2. Departamento de Matemática and IMAS UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab I, Int. Guiraldes 2160, (1428) Buenos Aires, Argentina;3. Departamento de Economía, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, (1428) Buenos Aires, Argentina;3. Department of Biochemistry and Biomedical Sciences and the Michael G. DeGroote Institute for Infectious Disease Research, McMaster University, Hamilton, Ontario L8S 4K1;4. Department of Biochemistry, Western University, London, Ontario N6A 3K7, Canada;1. School of Energy System Engineering, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, Republic of Korea;2. Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University E418 Scott Laboratory, 201W, 19th Ave, Columbus, OH 43210, USA.;1. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China;2. High-Tech Institute of Xi''an, Xi''an, 710025, China;3. Department of Computing, Hong Kong Polytechnic University, Hongkong, China |
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| Abstract: | Many real-world systems can be represented by bipartite networks. In a bipartite network, the nodes are divided into two disjoint sets, and the edges connect nodes that belong to different sets. Given a bipartite network (i.e. two-mode network) it is possible to construct two projected networks (i.e. one-mode networks) where each one is composed of only one set of nodes. While network analyses have focused on unipartite networks, considerably less attention has been paid to the analytical study of bipartite networks. Here, we analytically derive simple mathematical relationships that predict degree distributions of the projected networks by only knowing the structure of the original bipartite network. These analytical results are confirmed by computational simulations using artificial and real-world bipartite networks from a variety of biological and social systems. These findings offer in our view new insights into the structure of real-world bipartite networks. |
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