Related papers: A modularity based spectral method for simultaneou…
We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric…
Community detection methods can be used to explore the structure of complex systems. The well-known modular configurations in complex financial systems indicate the existence of community structures. Here we analyze the community properties…
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix $A$. The result exploits the Frobenius inner product between $A$ and a given rank-one landmark matrix $X$. Different choices for $X$ may…
With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newman's modularity…
Bipartite networks are a useful tool for representing and investigating interaction networks. We consider methods for identifying communities in bipartite networks. Intuitive notions of network community groups are made explicit using…
Using an intuitive concept of what constitutes a meaningful community, a novel metric is formulated for detecting non-overlapping communities in undirected, weighted heterogeneous networks. This metric, modularity density, is shown to be…
Modularity maximization is the most popular technique for the detection of community structure in graphs. The resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure, with tunable…
The "clumpiness" matrix of a network is used to develop a method to identify its community structure. A "projection space" is constructed from the eigenvectors of the clumpiness matrix and a border line is defined using some kind of angular…
In this paper we apply theoretical and practical results from facility location theory to the problem of community detection in networks. The result is an algorithm that computes bounds on a minimization variant of local modularity. We also…
Study of the cluster- or community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important…
Community detection is a commonly used technique for identifying groups in a network based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the network to be partitioned into a smaller…
Unknown node attributes in complex networks may introduce community structures that are important to distinguish from those driven by known attributes. We propose a block-corrected modularity that discounts given block structures present in…
Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a…
Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different…
Clustering and community detection with multiple graphs have typically focused on aligned graphs, where there is a mapping between nodes across the graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are numerous…
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph…
Graphs representing real world systems may be studied from their underlying community structure. A community in a network is an intuitive idea for which there is no consensus on its objective mathematical definition. The most used metric in…
Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have…
Community detection can reveal the underlying structure and patterns of complex networks, identify sets of nodes with specific functions or similar characteristics, and study the evolution process and development trends of networks. Despite…
Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the…