Related papers: Assortativity in Generalized Preferential Attachme…

Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have…

We introduce a new type of preferential attachment tree that includes choices in its evolution, like with Achlioptas processes. At each step in the growth of the graph, a new vertex is introduced. Two possible neighbor vertices are selected…

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…

The spatial preferential attachment (SPA) is a model for complex networks. In the SPA model, nodes are embedded in a metric space, and each node has a sphere of influence whose size increases if the node gains an in-link, and otherwise…

We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model…

Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…

In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a…

A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…

This paper expands the degree-based consideration of the preferential attachment growth process and applies five different connectivity criteria (node degree, clustering coefficient, betweenness centrality, closeness centrality, and…

A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…

Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…

Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models…

Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…

We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the…

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…

We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is…

We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of…

A general relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks.…

The classical preferential attachment model is sensitive to the choice of the initial configuration of the network. As the number of initial nodes and their degree grow, so does the time needed for an equilibrium degree distribution to be…

A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…