Related papers: Nonlinear preferential rewiring in fixed-size netw…
We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with $m$ randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a…
Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can…
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
Recently it has been shown that a large variety of different networks have power-law (scale-free) distributions of connectivities. We investigate the robustness of such a distribution in discrete threshold networks under neutral evolution.…
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…
We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
What happens when the time evolution of a fluctuating interface is interrupted with resetting to a given initial configuration after random time intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};~\alpha > 0$? For an…
We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
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…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
A new network evolution model is introduced in this paper. The model is based on co-operations of $N$ units. The units are the nodes of the network and the co-operations are indicated by directed links. At each evolution step $N$ units…
This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for…
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…
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…
In search of many social and economical systems, it is found that node strength distribution as well as degree distribution demonstrate the behavior of power-law with droop-head and heavy-tail. We present a new model for the growth of…