Related papers: Evolving small-world scale-free networks consist o…
We investigate the degree distribution $P(k)$ and the clustering coefficient $C$ of the line graphs constructed on the Erd\"os-R\'enyi networks, the exponential and the scale-free growing networks. We show that the character of the degree…
It has been observed that many complex real-world networks have certain properties, such as a high clustering coefficient, a low diameter, and a power-law degree distribution. A network with a power-law degree distribution is known as…
We investigate the number of maximal cliques, i.e., cliques that are not contained in any larger clique, in three network models: Erd\H{o}s-R\'enyi random graphs, inhomogeneous random graphs (also called Chung-Lu graphs), and geometric…
In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…
Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other…
We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected (``make friends with the friends of your…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on the structure generating distribution we obtain a scale…
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 formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…
We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out self-loops and multiple edges and allows for negative degree…
In this paper, we propose a general model for collaboration networks. Depending on a single free parameter "{\bf preferential exponent}", this model interpolates between networks with a scale-free and an exponential degree distribution. The…
Real-world networks often have power-law degrees and scale-free properties such as ultra-small distances and ultra-fast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the…
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 provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the…
Here, we propose a class of scale-free networks $G(t;m)$ with some intriguing properties, which can not be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including (i)…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
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.…
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.…