Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Efficient computation of functional brain networks: towards real-time functional connectivity

Abstract: Functional Connectivity has been demonstrated to be a key tool for unravelling how the brain balances functional segregation and integration properties while processing information. This work presents a set of open-source tools that significantly increase computational efficiency of some well-known connectivity indices and Graph-Theory measures. PLV, PLI, ImC and wPLI as Phase Synchronization measures, Mutual Information as an information theory based measure and Generalized Synchronization indices are computed much more efficiently than prior open-source available implementations. Furthermore, network theory related measures like Strength, Shortest Path Length, Clustering Coefficient and Betweenness Centrality are also implemented showing computational times up to thousands of times faster than most well-known implementations. Altogether, this work significantly expands what can be computed in feasible times, even enabling whole-head real-time network analysis of brain function.

Complex Networks and Symmetry I: A Review

Abstract: In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less developed. We argue that real networks, as any entity characterized by imperfections or errors, necessarily require a stochastic notion of invariance. We therefore propose a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective. The results discussed here and in a companion paper show that stochastic symmetry highlights the most informative topological properties of real networks, even in noisy situations unaccessible to exact techniques.

Accelerating, hyperaccelerating, and decelerating networks

Abstract: Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Key Sectors: A New Proposal from Network Theory

Abstract: Garcia Muniz A. S., Morillas Raya A. and Ramos Carvajal C. Key sectors: a new proposal from network theory, Regional Studies. There is a long tradition of studies in the input–output field for determining key sectors. Their analysis allows the identification of those sectors that affect the demand and supply system greatly, therefore constituting the basis for the growth and development of a territory. In order to pinpoint those sectors whose position is more relevant in the economy, a definition of centrality measures is proposed from network theory that is considered to be new in the input–output field. The definition is based on the consideration of three complementary characteristics: total effects, mediative effects and immediate effects. The term used for these measures is ‘multilevel indicators’ and these indicators have the enormous advantage of allowing different sized structures to be compared and the key sector concept to be approached from a relational and global viewpoint. Garcia Muniz A. S.,...

Structural determinants of criticality in biological networks

Abstract: Many adaptive evolutionary systems display spatial and temporal features, such as long-range correlations, typically associated with the critical point of a phase transition in statistical physics. Empirical and theoretical studies suggest that operating near criticality enhances the functionality of biological networks, such as brain and gene networks, in terms for instance of information processing, robustness, and evolvability. While previous studies have explained criticality with specific system features, we still lack a general theory of critical behavior in biological systems. Here we look at this problem from the complex systems perspective, since in principle all critical biological circuits have in common the fact that their internal organization can be described as a complex network. An important question is how self-similar structure influences self-similar dynamics. Modularity and heterogeneity, for instance, affect the location of critical points and can be used to tune the system toward criticality. We review and discuss recent studies on the criticality of neuronal and genetic networks, and discuss the implications of network theory when assessing the evolutionary features of criticality.