Related papers: Random Preferential Attachment Hypergraphs
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
Preferential attachment models form a popular class of growing networks, where incoming vertices are preferably connected to vertices with high degree. We consider a variant of this process, where vertices are equipped with a random initial…
We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…
A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…
We study a generalization of the affine preferential attachment model where triangles are randomly added to the graph. We show that the model exhibits an asymptotically power-law degree distribution with adjustable parameter $\gamma\in…
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…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
The mechanism of preferential attachment underpins most recent social network formation models. Yet few authors attempt to check or quantify assumptions on this mechanism. We call generalized preferential attachment any kind of preference…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…