Related papers: Logarithmic typical distances in preferential atta…
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…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…
We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of…
Several growth models have been proposed in the literature for scale-free complex networks, with a range of fitness-based attachment models gaining prominence recently. However, the processes by which such fitness-based attachment behaviour…
This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures,…
We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…
We study properties of some standard network models when the population is split into two types and the connection pattern between the types is varied. The studied models are generalizations of the Erd\H{o}s-R\'{e}nyi graph, the…
Generated networks are widely used in network-based research as a convenient simulation environment. Generating universal networks that more accurately reflect real-world patterns is a cornerstone task. This study proposes a vari-linear…
In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
We consider a preferential attachment process in which a multigraph is built one node at a time. The number of edges added at stage $t$, emanating from the new node, is given by some prescribed function $f(t)$, generalising a model…
A random k-out mapping (digraph) on [n] is generated by choosing k random images of each vertex one at a time, subject to a "preferential attachment" rule: the current vertex selects an image i with probability proportional to a given…
We consider the random walk attachment graph introduced by Saram\"{a}ki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge. We show that if the length…
Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…
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…
We study a random graph $G_n$, which combines aspects of geometric random graphs and preferential attachment. The resulting random graphs have power-law degree sequences with finite mean and possibly infinite variance. In particular, the…
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…
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…