Related papers: Simplex triangulation induced scale-free networks
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained…
We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…
We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…
We suggest a method for embedding scale-free networks, with degree distribution P(k) k^-lambda, in regular Euclidean lattices. The embedding is driven by a natural constraint of minimization of the total length of the links in the system.…
A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e.…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can…
We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule,…
Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is…