Abstract
BackgroundThe detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Since the adoption of modularity as a measure of network topological properties, several methodologies for the discovery of community structure based on modularity maximisation have been developed. However, satisfactory partitions of large graphs with modest computational resources are particularly challenging due to the NP-hard nature of the related optimisation problem. Furthermore, it has been suggested that optimising the modularity metric can reach a resolution limit whereby the algorithm fails to detect smaller communities than a specific size in large networks.ResultsWe present a novel solution approach to identify community structure in large complex networks and address resolution limitations in module detection. The proposed algorithm employs modularity to express network community structure and it is based on mixed integer optimisation models. The solution procedure is extended through an iterative procedure to diminish effects that tend to agglomerate smaller modules (resolution limitations).ConclusionsA comprehensive comparative analysis of methodologies for module detection based on modularity maximisation shows that our approach outperforms previously reported methods. Furthermore, in contrast to previous reports, we propose a strategy to handle resolution limitations in modularity maximisation. Overall, we illustrate ways to improve existing methodologies for community structure identification so as to increase its efficiency and applicability.
Highlights
The detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences
The application of iMod to detect modules and ResMod to correct for potential resolution limitations is illustrated through a number of real network examples
All implementations were performed in GAMS (General Algebraic Modeling System) [39] and mathematical models (MINLP and mixed integer quadratic programming (MIQP)) are solved using SBB [40] and CPLEX [41] mixed integer optimisation solvers with computational limit of 3600 seconds, where necessary
Summary
The detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Networks - i.e. groups of entities (nodes or vertices) pairs of which are linked through a form of common property (edges or links) - have formed an efficient representation framework for a variety of complex systems such as social groupings and internet connectivity [1]. Community structures or modules are defined when a larger density of links exists within a specific part of the network than outside it [9]. Each of such modules can be regarded as a discrete entity whose function or properties are in some way separable from other modules. The analysis of pairwise or even longer-range relationships in networks can reveal how preferential attachment of new nodes influences community structure [13,14], giving rise to small-world or scale-free architectures [15]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
