Related papers: Generalized Mittag Leffler distributions arising a…

We consider here the recently proposed closed form formula in terms of the Meijer G-functions for the probability density functions $g_\alpha(x)$ of one-sided L\'evy stable distributions with rational index $\alpha=l/k$, with $0<\alpha<1$.…

We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…

The S-metric has grown popular in network studies, as a measure of ``scale-freeness'' restricted to the collection G(D) of connected graphs with a common degree sequence D=(d_1,\ldots,d_n). The calculation of S depends on the maximum…

We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…

We consider some fractional extensions of the recursive differential equation governing the Poisson process, by introducing combinations of different fractional time-derivatives. We show that the so-called "Generalized Mittag-Leffler…

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…

Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or…

We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $\kappa $. Using very simple rules for forming such preferred degree networks, we find…

We study the percolation phase transition on preferential attachment models, in which vertices enter with $m$ edges and attach proportionally to their degree plus $\delta$. We identify the critical percolation threshold as…

We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…

Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…

The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized…

We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…

There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…

We consider the dimer model on piecewise Temperleyan, simply connected domains, on families of graphs which include the square lattice as well as superposition graphs. We focus on the spanning tree $\mathcal{T}_\delta$ associated to this…

We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there…

We investigate structural properties of large, sparse random graphs through the lens of "sampling convergence" (Borgs et. al. (2017)). Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a…

Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random…

We study the Ising model on affine preferential attachment models with general parameters. We identify the thermodynamic limit of several quantities, arising in the large graph limit, such as pressure per particle, magnetisation, and…

We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge…