Related papers: About Weighted Random Sampling in Preferential Att…
Link prediction is a technique that uses the topological information in a given network to infer the missing links in it. Since past research on link prediction has primarily focused on enhancing performance for given empirical systems,…
Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…
We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network…
For a sequence of random graphs, the limit law we refer to is the existence of a limiting probability of any graph property that can be expressed in terms of predicate logic. A zero-one limit law is shown by Shelah and Spencer for…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We study the Tree Builder Random Walk: a randomly growing tree, built by a walker as she is walking around the tree. Namely, at each time $n$, she adds a leaf to her current vertex with probability $p_n \asymp n^{-\gamma}$, $\gamma\in…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…
Most of the networks observed in real life obey power-law degree distribution. It is hypothesized that the emergence of such a degree distribution is due to preferential attachment of the nodes. Barabasi-Albert model is a generative…
In many networks of scientific interest we know that the link between any pair of vertices conforms to a specific probability, such as the link probability in the Barab\'asi-Albert scale-free networks. Here we demonstrate how the…
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by…
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…
The Asymmetric BA model extends the Barab\'asi-Albert scale-free network model by introducing a parameter $\omega$. As $\omega$ varies, the model transitions through different network structures: an extended lattice at $\omega = -1$, a…
We consider the problem of finding the initial vertex (Adam) in a Barab\'asi--Albert tree process $(\mathcal{T}(n) : n \geq 1)$ at large times. More precisely, given $ \varepsilon>0$, one wants to output a subset $ \mathcal{P}_{…
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
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…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
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…
Sensitivity analyses reveal the influence of various modeling choices on the outcomes of statistical analyses. While theoretically appealing, they are overwhelmingly inefficient for complex Bayesian models. In this work, we propose…
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…