Related papers: Analytic solution for preferential attachment prob…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
We consider a simple Preferential Attachment graph process, which begins with a finite graph, and in which a new $(t+1)$st vertex is added at each subsequent time step $t$, and connected to each previous vertex $u \leq t$ with probability…
We consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau>2$. For all subgraphs $H$, we find the scaling of the expected number of subgraphs as a power of the number of vertices. We prove our…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…
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 give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…
We study the following preferential attachment variant of the classical Erdos-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly…
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…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
Preferential attachment lies at the heart of many network models aiming to replicate features of real world networks. To simulate the attachment process, conduct statistical tests, or obtain input data for benchmarks, efficient algorithms…
The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends…