Related papers: A Classification of Isomorphism-Invariant Random D…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
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…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…
Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph.…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
We describe a general approach of determining the distribution of spanning subgraphs in the random graph $\G(n,p)$. In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The ring of graph invariants is spanned by the basic graph invariants which calculate the number of subgraphs isomorphic to a given graph in other graphs. These subgraphs counting invariants are not algebraically independent. In our view…
Let $G$ be a group. The directed endomorphism graph, \dend of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex `$a$' to the vertex `$\, b$' $(a \neq b) $ if and only if there exists an endomorphism on…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
In this paper we extend the classical notion of digraphical and graphical regular representation of a group and we classify, by means of an explicit description, the finite groups satisfying this generalization. A graph or digraph is called…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
The random ordered graph is the up to isomorphism unique countable homogeneous linearly ordered graph that embeds all finite linearly ordered graphs. We determine the reducts of the random ordered graph up to first-order interdefinability.