Related papers: Correlation between clustering and degree in affil…
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that…
We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…
Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree…
Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…
In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation…
We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter $ \alpha$. We prove that, with high probability, the node degrees satisfy the following ordering property: the…
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
In this work we analyze basic properties of Random Apollonian Networks \cite{zhang,zhou}, a popular stochastic model which generates planar graphs with power law properties. Specifically, let $k$ be a constant and $\Delta_1 \geq \Delta_2…
The article deals with two classes of growing random graphs following the preferential attachment rule with a linear weight function, L-graphs, and hybrid Pennock graphs. We determine the exact final vertex degree distribution and the exact…