Related papers: Primitive operations for the construction and reor…
If we are given a connected finite graph $G$ and a subset of its vertices $V_{0}$, we define a distance-residual graph as a graph induced on the set of vertices that have the maximal distance from $V_{0}$. Some properties and examples of…
We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
We consider the problem of transforming a given graph $G_s$ into a desired graph $G_t$ by applying a minimum number primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each…
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…
A group $G$ of permutations of a set $\Omega$ is {\em primitive} if it acts transitively on $\Omega$, and the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. A graph $\Gamma$ is {\em primitive}…
A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
An infinite periodic framework in the plane can be represented as a framework on a torus, using a $\mathbb Z^2$-labelled gain graph. We find necessary and sufficient conditions for the generic minimal rigidity of frameworks on the…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to…
This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…