Related papers: Exactly solvable scale-free network model
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms…
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…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
We report on exact results for the degree $K$, the diameter $D$, the clustering coefficient $C$, and the betweenness centrality $B$ of a hierarchical network model with a replication factor $M$. Such quantities are calculated exactly with…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
There are many networks in real life which exist as form of Scale-free networks such as World Wide Web, protein-protein interaction network, semantic networks, airline networks, interbank payment networks, etc. If we want to analyze these…
Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…
We have studied nucleation dynamics of the Ising model in scale-free networks with degree distribution $P(k)\sim k^{-\gamma}$ by using forward flux sampling method, focusing on how the network topology would influence the nucleation rate…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…
In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to…
We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes $N$ and a given cost--which we take as the average number of connections per node $\kav$. We find that the…
Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski…
We consider two-source two-destination (i.e., two-unicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous…