Network theory

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

Spatially extended balanced networks without translationally invariant connectivity.

Abstract: Networks of neurons in the cerebral cortex exhibit a balance between excitation (positive input current) and inhibition (negative input current). Balanced network theory provides a parsimonious mathematical model of this excitatory-inhibitory balance using randomly connected networks of model neurons in which balance is realized as a stable fixed point of network dynamics in the limit of large network size. Balanced network theory reproduces many salient features of cortical network dynamics such as asynchronous-irregular spiking activity. Early studies of balanced networks did not account for the spatial topology of cortical networks. Later works introduced spatial connectivity structure, but were restricted to networks with translationally invariant connectivity structure in which connection probability depends on distance alone and boundaries are assumed to be periodic. Spatial connectivity structure in cortical network does not always satisfy these assumptions. We use the mathematical theory of integral equations to extend the mean-field theory of balanced networks to account for more general dependence of connection probability on the spatial location of pre- and postsynaptic neurons. We compare our mathematical derivations to simulations of large networks of recurrently connected spiking neuron models.

A Graph-theoretic Method for Identification of Electric Power Distribution System Topology

Abstract: In this paper, we present a graph-theoretic method for identification of the topology of electric power distribution system based on the real-time measurements. Instead of relying on the electric-circuit based approaches, this new approach utilizes the principles of network theory to find the connecting structure or topology of a distribution system. First, we put forth the theoretical foundation for the proposed approach. Second, applying some principles and methods of network theory, we develop and present the process of topology identification. Third, the algorithm for practical implementation of the concepts is offered with an illustrative example. Finally, the potential applications and the insights obtained from this work are discussed.

Social Networks and Systems Theory

Abstract: This paper provides a critical assessment of the conceptions of social networks in systems theory. There are two main solutions to the problem: treating networks as systems, or denying them that status. The last group conceives networks as structural couplings (Kamper and Schmidt) or as forms (Fuhse). Among the first group, Luhmann has used the concept to describe the particularities of the societal structure of underdeveloped regions, but he did not delve into a theoretical characterization of the concept. Teubner’s version also remained associated with a particular episode, providing no general network theory. Bommes and Tacke establish reciprocity as the central mechanism, which relates different addresses (persons or organizations) through a non-specific future promise of a service in return for a favor. The analysis shows that this account provides the most complete version of the concept, remaining fully compatible with systems theory.

Hierarchical Community Structure in Complex (Social) Networks

Abstract: The investigation of community structure in networks is a task of great importance in many disciplines, namely physics, sociology, biology and computer science where systems are often represented as graphs. One of the challenges is to find local communities from a local viewpoint in a graph without global information in order to reproduce the subjective hierarchical vision for each vertex. In this paper we present the improvement of an information dynamics algorithm in which the label propagation of nodes is based on the Markovian flow of information in the network under cognitive-inspired constraints \cite{Massaro2012}. In this framework we have introduced two more complex heuristics that allow the algorithm to detect the multi-resolution hierarchical community structure of networks from a source vertex or communities adopting fixed values of model's parameters. Experimental results show that the proposed methods are efficient and well-behaved in both real-world and synthetic networks.

Shifting Our Gaze: Relational Space in Professional Learning Network Research

Abstract: Reflecting on professional learning networks (PLN) in rural and equity-seeking spaces, the authors foreground the importance of “relational space” in studying PLNs in this commentary. The authors argue that while the complexity of taking a relational approach is challenging, it offers an important and necessary perspective, one which is often implicit in the studies featured in this book but not explicitly considered. The chapter is organized around three broad concepts from social network theory – boundedness, connectedness, and mutuality – which serve as starting points for shifting our gaze from formal system structures to more deeply interrogating the informal relational spaces within PLNs. The authors conclude with a call to make use of network theory and methods on their own, and in complement to other literatures, to do so.