Related papers: Isotemporal classes of n-gons
Temporal graphs are a special class of graphs for which a temporal component is added to edges, that is, each edge possesses a set of times at which it is available and can be traversed. Many classical problems on graphs can be translated…
In this paper, we show that for an $n$-vertex graph $G$ of genus $g$, the edge expansion of $G$ can be determined in time $n^{O(g^2)}$. We show that the same is true for various other similar measures of edge connectivity.
We study the complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W_n and the number of edges H_n of the minimal weight path between two distinct…
In this work we consider \emph{temporal networks}, i.e. networks defined by a \emph{labeling} $\lambda$ assigning to each edge of an \emph{underlying graph} $G$ a set of \emph{discrete} time-labels. The labels of an edge, which are natural…
We propose a new Graph Neural Network that combines recent advancements in the field. We give theoretical contributions by proving that the model is strictly more general than the Graph Isomorphism Network and the Gated Graph Neural…
Temporal networks, defined as sequences of time-aggregated adjacency matrices, sample latent graph dynamics and trace trajectories in graph space. By interpreting each adjacency matrix as a different time snapshot of a scalar field,…
Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA '14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit…
Let $\Gamma$ be a multigraph with for each vertex a cyclic order of the edges incident with it. For $n \geq 3$, let $D_{2n}$ be the dihedral group of order $2n$. Define $\mathbb{D} := \{(\begin{smallmatrix} 1 & a \\ 0 & 1 \end{smallmatrix})…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
We define a new family of graph invariants, studying the topology of the moduli space of their geometric realizations in Euclidean spaces, using a limiting procedure reminiscent of Floer homology. Given a labeled graph $G$ on $n$ vertices…
We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding…
Edges in real-world graphs are typically formed by a variety of factors and carry diverse relation semantics. For example, connections in a social network could indicate friendship, being colleagues, or living in the same neighborhood.…
Despite the success of graph neural networks (GNNs) in various domains, they exhibit susceptibility to adversarial attacks. Understanding these vulnerabilities is crucial for developing robust and secure applications. In this paper, we…
This paper introduces a new class of efficient inter connection networks called as M-graphs for large multi-processor systems.The concept of M-matrix and M-graph is an extension of Mn-matrices and Mn-graphs.We analyze these M-graphs…
In this paper I introduce a framework for modeling temporal communication networks and dynamical processes unfolding on such networks. The framework originates from the realization that there is a meaningful division of temporal…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
In this work, we present a method for node embedding in temporal graphs. We propose an algorithm that learns the evolution of a temporal graph's nodes and edges over time and incorporates this dynamics in a temporal node embedding framework…
Graph Neural Networks (GNNs) have been highly successful for the node classification task. GNNs typically assume graphs are homophilic, i.e. neighboring nodes are likely to belong to the same class. However, a number of real-world graphs…
A graph is closed when its vertices have a labeling by $[n]$ such that the binomial edge ideal $J_G$ has a quadratic Gr\"{o}bner basis with respect to the lexicographic order induced by $x_1 > \cdots > x_n > y_1> \cdots > y_n$. In this…
We develop a structural approach to simultaneous embeddability in temporal sequences of graphs, inspired by graph minor theory. Our main result is a classification theorem for 2-connected temporal sequences: we identify five obstruction…