Analysis of the structure of complex networks at different resolution levels

Abstract

Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for a partition of a network into modules. Recently some authors [1,2] have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows to find the exact splits reported in the literature, as well as the substructure beyond the actual split.

23 pages, 5 figures

References in corpus (24)

• Community structure in social and biological networks
• Finding and evaluating community structure in networks
• Modularity and community structure in networks
• Finding community structure in very large networks
• Fast algorithm for detecting community structure in networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Finding community structure in networks using the eigenvectors of matrices
• Cooperative Game Theory Approaches for Network Partitioning
• Functional cartography of complex metabolic networks
• Resolution limit in community detection
• Comparing community structure identification
• Analysis of weighted networks
• Hierarchical Organization in Complex Networks
• Statistical Mechanics of Community Detection
• The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
• Community detection in complex networks using Extremal Optimization
• Community Structure in Jazz
• Synchronization reveals topological scales in complex networks
• Extracting the hierarchical organization of complex systems
• Subnetwork hierarchies of biochemical pathways
• Size reduction of complex networks preserving modularity
• Modularity and Extreme Edges of the Internet
• Limited resolution in complex network community detection with Potts model approach
• Synchronization processes in complex networks

Cited by in corpus (99)

• Fast unfolding of communities in large networks
• Community detection in graphs
• Synchronization in complex networks
• Detecting the overlapping and hierarchical community structure of complex networks
• Community detection in networks: A user guide
• The performance of modularity maximization in practical contexts
• Line Graphs, Link Partitions and Overlapping Communities
• Limits of modularity maximization in community detection
• Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
• Laplacian Dynamics and Multiscale Modular Structure in Networks
• Narrow scope for resolution-limit-free community detection
• Community detection in networks: Modularity optimization and maximum likelihood are equivalent
• Community Detection via Maximization of Modularity and Its Variants
• Analysis of community structure in networks of correlated data
• Parsimonious module inference in large networks
• Multiresolution community detection for megascale networks by information-based replica correlations
• A General Optimization Technique for High Quality Community Detection in Complex Networks
• Local resolution-limit-free Potts model for community detection
• Tolerating the Community Detection Resolution Limit with Edge Weighting
• Communities, Knowledge Creation, and Information Diffusion
• Mixing local and global information for community detection in large networks
• Community detection for correlation matrices
• Line Graphs of Weighted Networks for Overlapping Communities
• Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks
• Fuzzy overlapping communities in networks
• Quantifying and identifying the overlapping community structure in networks
• Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity
• Improved community structure detection using a modified fine tuning strategy
• Understanding mobility in a social petri dish
• Multiscale unfolding of real networks by geometric renormalization
• Social significance of community structure: Statistical view
• Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs
• Spectral methods for the detection of network community structure: a comparative analysis
• Z-score-based modularity for community detection in networks
• How humans learn and represent networks
• Spectral tripartitioning of networks
• Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
• Statistical inference of assortative community structures
• Resolving Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations
• Core-periphery structure requires something else in the network
• Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007--2008 credit crisis
• Hierarchical multiresolution method to overcome the resolution limit in complex networks
• Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths
• Community structure and the evolution of interdisciplinarity in Slovenia's scientific collaboration network
• Uncovering the community structure associated with the diffusion dynamics of networks
• Potts model based on a Markov process computation solves the community structure problem effectively
• Covariance, correlation matrix and the multi-scale community structure of networks
• Collectively optimal routing for congested traffic limited by link capacity
• Multiscale dynamical embeddings of complex networks
• Random matrix analysis of localization properties of Gene co-expression network
• Link-Prediction Enhanced Consensus Clustering for Complex Networks
• Detecting communities of triangles in complex networks using spectral optimization
• Post-processing partitions to identify domains of modularity optimization
• Revealing In-Block Nestedness: detection and benchmarking
• Limitation of multi-resolution methods in community detection
• Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature
• Network community detection using modularity density measures
• Soft communities in similarity space
• A Replica Inference Approach to Unsupervised Multi-Scale Image Segmentation
• Multilayer Network Science: from Cells to Societies
• Finding network communities using modularity density
• Multi-resolution community detection based on generalized self-loop rescaling strategy
• Optimal map of the modular structure of complex networks
• Spectral Properties of Directed Random Networks with Modular Structure
• Contagion processes on the static and activity driven coupling networks
• Analysis of stability of community structure across multiple hierarchical levels
• Spectral analysis of deformed random networks
• Revealing and exploiting hierarchical material structure through complex atomic networks
• Detecting modules in dense weighted networks with the Potts method
• Hierarchical mutual information for the comparison of hierarchical community structures in complex networks
• Entropic one-class classifiers
• Hierarchical organization of brain functional network during visual task
• Mesoscopic analysis of networks: applications to exploratory analysis and data clustering
• Community detection in networks via nonlinear modularity eigenvectors
• Core of communities in bipartite networks
• Identifying multi-scale communities in networks by asymptotic surprise
• Consistency landscape of network communities
• An algebraic analysis of the graph modularity
• Community detection based on significance optimization in complex networks
• Global disorder transition in the community structure of large-q Potts systems
• Finding overlapping communities in networks using evolutionary method
• Community structure revealed by phase locking
• Unsupervised clustering analysis: a multiscale complex networks approach
• Link community detection through global optimization and the inverse resolution limit of partition density
• Modularity in Multilayer Networks using Redundancy-based Resolution and Projection-based Inter-Layer Coupling
• Structural patterns in complex systems using multidendrograms
• Generalized Markov stability of network communities
• Mining the modular structure of protein interaction networks
• Communities in C.elegans connectome through the prism of non-backtracking walks
• Criterions for locally dense subgraphs
• Local multiresolution order in community detection
• Modeling international crisis synchronization in the World Trade Web
• Stochastic Block Models are a Discrete Surface Tension
• The Asymptotic Distribution of Modularity in Weighted Signed Networks
• Multilayer Modularity Belief Propagation To Assess Detectability Of Community Structure
• Comprehensive spectral approach for community structure analysis on complex networks
• Structure and evolution of a European Parliament via a network and correlation analysis
• Exploring 3D community inconsistency in human chromosome contact networks
• Symmetrical SyncMap for Imbalanced General Chunking Problems