Related papers: Generating random bigraphs with preferential attac…
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in…
In this paper, we introduce a novel approach for generating random elements of a finite group given a set of generators of that. Our method draws upon combinatorial group theory and automata theory to achieve this objective. Furthermore, we…
We use Stein's method to obtain distributional approximations of subgraph counts in the uniform attachment model or random directed acyclic graph; we provide also estimates of rates of convergence. In particular, we give uni- and…
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…
This note describes a new approach to classifying graphs that leverages graph generative models (GGM). Assuming a GGM that defines a joint probability distribution over graphs and their class labels, I derive classification formulas for the…
Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
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…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824-827].…
We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed…
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…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
In order to study some sets of probabilities, called induced averages by J. Ecalle, F. Menous introduces two grafting operators $ B^{+} $ and $ B^{-} $. With these two operators, we construct Hopf algebras of rooted and ordered trees $…
Structure aware graph generation aims to generate graphs that satisfy given topological properties. It has applications in domains such as drug discovery, social network modeling, and knowledge graph construction. Unlike existing methods…
Bipartite graph embedding has recently attracted much attention due to the fact that bipartite graphs are widely used in various application domains. Most previous methods, which adopt random walk-based or reconstruction-based objectives,…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
Given a set of attributed subgraphs known to be from different classes, how can we discover their differences? There are many cases where collections of subgraphs may be contrasted against each other. For example, they may be assigned…