Related papers: On the evolution in the configuration model
A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The…
We introduce the Iterated Global model as a deterministic graph process that simulates several properties of complex networks. In this model, for every set $S$ of nodes of a prescribed cardinality, we add a new node that is adjacent to…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…
Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…
We characterize which graph invariants are partition functions of an edge-coloring model over the complex numbers, in terms of the rank growth of associated `connection matrices'.
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles' control parameters relative to the number of…
We consider the uniform random $d$-regular graph on $N$ vertices, with $d \in [N^\alpha, N^{2/3-\alpha}]$ for arbitrary $\alpha > 0$. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
We look at the evolution through rewiring of the degree distribution of a network so the number edges is constant. This is exactly equivalent to the evolution of probability distributions in models of cultural transmission with drift and…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which…
Machine learning models for graphs in real-world applications are prone to two primary types of uncertainty: (1) those that arise from incomplete and noisy data and (2) those that arise from uncertainty of the model in its output. These…