Related papers: Phase Transition on The Degree Sequence of a Mixed…
We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
The problem of efficiently sampling from a set of (undirected, or directed) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
The one-dimensional kinetic contact process with parallel update is introduced and studied by Monte Carlo simulations. This process is proposed to describe the plant population replication and epidemic disease spreading among them. The…
In this paper we study the degree sequence of the permutation graph $G_{\pi_n}$ associated with a sequence $\pi_n\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian…
In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…
We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…
In this paper we introduce the perturbed version of the Barab\'asi-Albert random graph with multiple type edges and prove the existence of the (generalized) asymptotic degree distribution. Similarly to the non-perturbed case, the asymptotic…
We study the spreading dynamics on graphs with a power law degree distribution p_k ~ k^-gamma with 2<gamma<3, as an example of a branching process with diverging reproductive number. We provide evidence that the divergence of the second…
Continuous-time branching processes (CTBPs) are powerful tools in random graph theory, but are not appropriate to describe real-world networks, since they produce trees rather than (multi)graphs. In this paper we analyze collapsed branching…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…