We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models. Moreover, clustering coefficient of these graphs can also be controlled. We propose a concrete flexible model from our class and provide an efficient algorith...

We introduce a minimal model of growing small-world network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially with degree and average clustering coefficient C = 3 2 ln3− 1 ≈ 0.6479, which are in good agreement with the numerical simulations. We also prove that the i...

We propose a novel method to generate scale-free networks with discretely tunable clustering coefficient in order to model real social networks. Recently several methods were introduced to generate networks with power law degree distribution. Most of them are based on preferential attachment, but in these networks the average clustering coefficient is low opposite to the real social networks. B...

This work is a modeling of evolutionary networks embedded in one or two dimensional configuration space. The evolution is based on two attachments depending on degree and spatial distance. The probability for a new node n to connect with a previous node i at distance r ni follows a k i  j k j + (1 − a) r −α ni  j r −α nj , where k i is the degree of node i, α and a are tunable parameters. In ...

Available online xxxx Keywords: Defective renewal equation Compound geometric distribution Ladder height Lundberg's fundamental equation Generalized adjustment coefficient Cramer's asymptotic ruin formula Esscher transform Last interclaim time NWU NBU a b s t r a c t The structure of various Gerber–Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and...

The algorithm of Minh as in [Minh (1988)] was used to generate variates having a gamma distribution with shape parameter a>1 only. In this paper, a method, which is the improvement of the algorithm of Minh is introduced for the generation of independent random variables from a gamma distribution with all values of shape parameter and is compared with the method of Marsaglia and Tsang. By means ...

We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean first passage time (MFPT) which appears always finite, also for the subdiffusive case. Then, for the case of the jumping-size distribution in form of the Lévy di...

The content-based network model which we have proposed[2] offers possibilities to investigate processes based on molecular recognition and binding. In particular, it seems to be a promising model of gene regulation in its different respects such as topology and dynamics. Random Boolean Dynamics on our content-based network will be introduced and our results will be presented. The network has a ...

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador” nodes and l of each ambassador’s descendants where m and l are random variables selected from any choice of d...

We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree correlations. We introduce the Gaussian Latent Position Model, and derive analytic expressions and asymptotic approximations for its network properties. We ...