Related papers: Recursive weighted treelike networks
Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barab\'asi \etal, Physica A, 299, 3 (2001)] and…
According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their…
Real-world growth processes and scalings have been broadly categorized into three growth regimes with distinctly different properties and driving forces. The first two are characterized by a positive and constant feedback between growth and…
We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for…
We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses…
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…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
In this paper, a simply rule that generates scale-free networks with very large clustering coefficient and very small average distance is presented. These networks are called {\bf Multistage Random Growing Networks}(MRGN) as the adding…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$.…
We analyze the degree distribution's cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices $N$ is ruled by the topological constraints induced by the connectivity structure of the network.…
Since network motifs are an important property of networks and some networks have the behaviors of rewiring or reducing or adding edges between old vertices before new vertices entering the networks, we construct our non-randomized model…
We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…