Related papers: Generating random bigraphs with preferential attac…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
Collections of journal papers, often referred to as 'citation networks', can be modeled as a collection of coupled bipartite networks which tend to exhibit linear growth and preferential attachment as papers are added to the collection.…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment},…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover…
We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…
Bigraph reactive systems offer a powerful and flexible mathematical framework for modelling both spatial and non-spatial relationships between agents, with practical applications in domains such as smart technologies, networks, sensor…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
This paper introduces a novel hypergraph classification algorithm. The use of hypergraphs in this framework has been widely studied. In previous work, hypergraph models are typically constructed using distance or attribute based methods.…
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
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…
In this paper, we present a model based on relations for bigraphical reactive systems [Milner09]. Its defining characteristics are that validity and reaction relations are captured as traces in a multi-set rewriting system. The relational…
We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…
Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…