Modularity and community detection in bipartite networks.

By Michael J. Barber. Physical review. E, Statistical, nonlinear, and soft matter physics, 2007

743 citations recorded by the source corpus.

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity. The bipartite modularity is presented in terms of a modularity matrix B; some key properties of the eigenspectrum of B are identified and used to describe an algorithm for identifying modules in bipartite networks. The algorithm is based on the idea that the modules in the two parts of the network are dependent, with each part mutually being used to induce the vertices for the other part into the modules. We apply the algorithm to real-world network data, showing that the algorithm successfully identifies the modular structure of bipartite networks.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2d0851086cdc8b2300b307335dea01c2260e06e0

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In Statistical and Nonlinear Physics

Citations in the corpus

Identifying compartments in presence–absence matrices and bipartite networks: insights into modularity measures (2013, methodology): “This last measure has been proposed by Barber (2007) although it was defined through a different demonstration than presented below.”
A classification for community discovery methods in complex networks (2011, background): “’s work by allowing multidimensional paths for the random walker ([102]), considering the different connection types with different weights ([103]), and a different spread of these weights among the dimensions ([104]).”
Global patterns of interaction specialization in bird–flower networks (2017, methodology): “Binary modularity was measured using the Barber metric (Barber, 2007), with simulated annealing as the search algorithm in the MODULAR software (Marquitti et al.”
A method for detecting modules in quantitative bipartite networks (2013, methodology): “Most recently, Thébault (2013) investigated, through simulations, the ability of three modularity measures (those of Newman & Girvan, 2004; Guimerà et al. , 2007; Barber, 2007) to identify modules in binary bipartite networks and comes out in support of that of Guimerà et al. (2007).”
Structure–stability relationships in networks combining mutualistic and antagonistic interactions (2014, methodology): “Modularity Q is calculated using the formula developed for bipartite networks (Thébault 2013, Barber 2008).”
Generalist Species Have a Central Role In a Highly Diverse Plant–Frugivore Network (2016, methodology): “We performed 1000 iterations with a simulated annealing algorithm that uses a global optimization procedure to maximize the modularity function MB proposed by Barber (2007).”
Determinants of community structure in the global plankton interactome (2015, methodology): “rithm (84) in BiMAT with 100 permutations (preserving edge number and degree distribution) was significant, but not with the NTC”
Improved community detection in weighted bipartite networks (2016, background): “This is done by assessing the extent to which interactions in the network occur within modules rather than between modules, relative to a null model [6,7].”
Motif-based communities in complex networks (2007, background): “We remark that bipartite networks are characterized by the fact that any path with even length starting from a node of either class ends in the same class, due to the absence of internal edges in each class.”
Community detection in Social Media (2012, background): “A generalization of modularity was presented by Reichardt and Bornholdt (2006) and numerous variations of the concept have been introduced for computing modularity in weighted (Newman 2004b), directed (Arenas et al. 2007) and bipartite (Barber 2007) networks.”
Communities in Networks (2009, background): “However, there has been seemingly only limited work thus far on community finding that works directly on bipartite networks rather than on their unipartite projections [10,53,71,100].”
Community detection in networks: A user guide (2016, background): “Other choices of the null model term allow us to incorporate specific features of network structure, like bipartiteness [147], correlations [148], signed edges [149], space embeddedness [150], etc.”
Identifying Causes of Patterns in Ecological Networks: Opportunities and Limitations (2017, background): “There are variations on this formula; this one is apt for quantitative networks (i.e., with values other than 0 or 1 in the adjacency matrix) and extensions to bipartite networks (Barber 2007).”