Related papers: Scale-free Networks on Lattices

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…

Networks of disparate phenomena-- be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions-- exhibit broadly consistent architectural features. To explain this, we propose a new…

Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as…

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…

The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the…

We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting…

Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal and random lattices is studied. The adsorption process is modeled by using random sequential adsorption (RSA) algorithm. Objects are adsorbed on one-,…

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…

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…

Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…

Random scale-free networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scale-free…

A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…

We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for…

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…

We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…

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),…

We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…

Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such…

We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…