Related papers: An Exact, Linear Time Barab\'asi-Albert Algorithm
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…
The S-metric has grown popular in network studies, as a measure of ``scale-freeness'' restricted to the collection G(D) of connected graphs with a common degree sequence D=(d_1,\ldots,d_n). The calculation of S depends on the maximum…
Based on the concept and techniques of first-passage probability in Markov chain theory, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the…
There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…
Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully…
Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…
Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node…
The bigraph theory is a relatively young, yet formally rigorous, mathematical framework encompassing Robin Milner's previous work on process calculi, on the one hand, and provides a generic meta-model for complex systems such as multi-agent…
A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barab\'asi--Albert random graph model…
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 prove that the Barab\'asi-Albert model converges weakly to a set of generalized Yule models via an appropriate scaling. To pursue this aim we superimpose to its graph structure a suitable set of processes that we call the planted model…
The likelihood-free sequential Approximate Bayesian Computation (ABC) algorithms, are increasingly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over…
We prove the existence of a large complete subgraph w.h.p. in a preferential attachment random graph process with an edge-step. That is, we prove that the random graph $G_{t}$ produced by the so-called GLP model at time $t$ contains a…
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…
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…
Presented here is the explicit solution to the continuous time approximation of the Albert-Barab\'asi scale-free network model at any time t. The solution is found by recursively solving the differential equations via integrating factors,…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…
The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…
A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its…