Modular networks emerge from multiconstraint optimization

Abstract

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.

5 pages, 4 figures; Published version

References in corpus (19)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Community structure in social and biological networks
• Finding and evaluating community structure in networks
• Efficient Behavior of Small-World Networks
• Hierarchical organization of modularity in metabolic networks
• Functional cartography of complex metabolic networks
• Defining and identifying communities in networks
• Community detection in complex networks using Extremal Optimization
• Nonequilibrium phase transition in the coevolution of networks and opinions
• Optimal network topologies for local search with congestion
• Subnetwork hierarchies of biochemical pathways
• Entangled networks, synchronization, and optimal network topology
• Modularity and Extreme Edges of the Internet
• Optimization of Network Robustness to Waves of Targeted and Random Attack
• Community analysis in social networks
• Small-worlds: How and why
• Complexity vs stability in small-world networks
• Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics

Cited by in corpus (14)

• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Mesoscopic organization reveals the constraints governing C. elegans nervous system
• Community structure of complex software systems: Analysis and applications
• Organization of modular networks
• The strength of strong ties in scientific collaboration networks
• Modularity produces small-world networks with dynamical time-scale separation
• Mutation Rules and the Evolution of Sparseness and Modularity in Biological Systems
• Modular networks with hierarchical organization: The dynamical implications of complex structure
• Phase of Ising spins on modular networks analogous to social polarization
• Modular organization enhances the robustness of attractor network dynamics
• Social Climber attachment in forming networks produces phase transition in a measure of connectivity
• Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs
• From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems
• Mesoscopic architecture enhances communication across the Macaque connectome revealing structure-function correspondence in the brain