相关论文: High Dimensional Apollonian Networks
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving…
Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form $P(k) \propto e_q^{-k/\kappa}$, where the $q$-exponential…
We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…
We describe collaboration networks consisting of research projects funded by the European Union and the organizations involved in those projects. The networks are of substantial size and complexity, but are important to understand due to…
Clustering, a fundamental task in data science and machine learning, groups a set of objects in such a way that objects in the same cluster are closer to each other than to those in other clusters. In this paper, we consider a well-known…
We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…
Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on…
We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…
We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…
This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of…
Many real-world networks have high clustering among vertices: vertices that share neighbors are often also directly connected to each other. A network's clustering can be a useful indicator of its connectedness and community structure.…
What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks.…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our ``dense graphs''…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
We present the distance matrix evolution for different types of networks: exponential, scale-free and classical random ones. Statistical properties of these matrices are discussed as well as topological features of the networks. Numerical…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…