Related papers: Small-world networks and RNA secondary structures
While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is…
We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
In this paper, we studied the research areas of Chinese natural science basic research from a point view of complex network. Two research areas are considered to be connected if they appear in one fund proposal. The explicit network of such…
We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Recent renormalization group results predict non self averaging behaviour at criticality for relevant disorder. However, we find strong self averaging(SA) behaviour in the critical region of a quenched Ising model on an ensemble of…
Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc-…
We consider shallow (single hidden layer) neural networks and characterize their performance when trained with stochastic gradient descent as the number of hidden units $N$ and gradient descent steps grow to infinity. In particular, we…
In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…