Related papers: Strength Distribution in Derivative Networks
One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex…
Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…
Networked structure emerged from a wide range of fields such as biological systems, World Wide Web and technological infrastructure. A deeply insight into the topological complexity of these networks has been gained. Some works start to pay…
All crucial features of the recently observed real-world weighted networks are obtained in a model where the weight of a link is defined with a single non-linear parameter $\alpha$ as $w_{ij}=(s_is_j)^\alpha$, $s_i$ and $s_j$ are the…
We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the…
Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
Classical results on the statistical complexity of linear models have commonly identified the norm of the weights $\|w\|$ as a fundamental capacity measure. Generalizations of this measure to the setting of deep networks have been varied,…
We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
In this paper, we interpret Deep Neural Networks with Complex Network Theory. Complex Network Theory (CNT) represents Deep Neural Networks (DNNs) as directed weighted graphs to study them as dynamical systems. We efficiently adapt CNT…
Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so.…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…