Related papers: Scalable Generation of Scale-free Graphs

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…

Massive power-law graphs drive many fields: metagenomics, brain mapping, Internet-of-things, cybersecurity, and sparse machine learning. The development of novel algorithms and systems to process these data requires the design, generation,…

We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space and randomness complexities of such samplers. In the standard…

Autoregressive models excel in efficiency and plug directly into the transformer ecosystem, delivering robust generalization, predictable scalability, and seamless workflows such as fine-tuning and parallelized training. However, they…

We introduce AutoGraph, a scalable autoregressive model for attributed graph generation using decoder-only transformers. By flattening graphs into random sequences of tokens through a reversible process, AutoGraph enables modeling graphs as…

There has been a recent surge in learning generative models for graphs. While impressive progress has been made on static graphs, work on generative modeling of temporal graphs is at a nascent stage with significant scope for improvement.…

In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…

We extend our previous algorithm that generates all labeled graphs with a given graphical degree sequence to generate all labeled triangle-free graphs with a given graphical degree sequence. The algorithm uses various pruning techniques to…

Learning graph generative models is a challenging task for deep learning and has wide applicability to a range of domains like chemistry, biology and social science. However current deep neural methods suffer from limited scalability: for a…

We have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barab\'asi-Albert (BA) algorithm, networks were generated using four additional…

We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…

Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…

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…

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…

The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms…

We present a novel algorithm that generates scale free small world graphs such as those found in the World Wide Web,social and metabolic networks. We use the generated graphs to study the dynamics of a realistic search strategy on the…

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…

Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…

We numerically investigate the scale-free network model of Barab{\'a}si and Albert [A. L. Barab{\'a}si and R. Albert, Science {\bf 286}, 509 (1999)] through the use of various path finding strategies. In real networks, global network…

The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their…