On bipartization of networks

Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover structural properties of a network. A network is said to be bipartite if its nodes can be subdivided into two nonempty sets such that there are no edges between nodes in the same set. It is a difficult task to determine the closest bipartite network to a given network. This paper describes how a given network can be approximated by a bipartite one by solving a sequence of fairly simple optimization problems. We also show how the same procedure can be used to detect the presence of a large anti-community in a network and to identify it.

[1]  Giuseppe Rodriguez,et al.  PQser: a Matlab package for spectral seriation , 2017, Numerical Algorithms.

[2]  Dario Fasino,et al.  A modularity based spectral method for simultaneous community and anti-community detection , 2017, ArXiv.

[3]  Jesús Gómez-Gardeñes,et al.  Network bipartivity and the transportation efficiency of European passenger airlines , 2016 .

[4]  Ernesto Estrada,et al.  A First Course in Network Theory , 2015 .

[5]  Ling Chen,et al.  Anti-modularity and anti-community detecting in complex networks , 2014, Inf. Sci..

[6]  Lothar Reichel,et al.  Tridiagonal Toeplitz matrices: properties and novel applications , 2013, Numer. Linear Algebra Appl..

[7]  Ernesto Estrada,et al.  The Structure of Complex Networks: Theory and Applications , 2011 .

[8]  D. Higham,et al.  Discovering bipartite substructure in directed networks , 2011, LMS J. Comput. Math..

[9]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[10]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[11]  Jure Leskovec,et al.  Statistical properties of community structure in large social and information networks , 2008, WWW.

[12]  Jiming Liu,et al.  Community Mining from Signed Social Networks , 2007, IEEE Transactions on Knowledge and Data Engineering.

[13]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[15]  D. Bu,et al.  Topological structure analysis of the protein-protein interaction network in budding yeast. , 2003, Nucleic acids research.

[16]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[17]  Martin G. Everett,et al.  Models of core/periphery structures , 2000, Soc. Networks.

[18]  R. Roth,et al.  On the eigenvectors belonging to the minimum eigenvalue of an essentially nonnegative symmetric matrix with bipartite graph , 1989 .

[19]  N. Higham.  MATRIX NEARNESS PROBLEMS AND APPLICATIONS , 1989 .

[20]  The distance between the eigenvalues of Hermitian matrices , 1986 .

[21]  William M. Kantor,et al.  The mathematics of perfect shuffles , 1983 .

[22]  G. Golub.  Matrix computations , 1983 .

[23]  Mihalis Yannakakis,et al.  Edge-Deletion Problems , 1981, SIAM J. Comput..