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A temporal graph is an undirected graph $G=(V,E)$ along with a function that assigns a time-label to each edge in $E$. A path in $G$ with non-decreasing time-labels is called temporal path and the distance from $u$ to $v$ is the minimum…

Data Structures and Algorithms · Computer Science 2022-06-23 Davide Bilò , Gianlorenzo D'Angelo , Luciano Gualà , Stefano Leucci , Mirko Rossi

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…

Social and Information Networks · Computer Science 2022-10-18 Lucas Lacasa , Jorge P. Rodriguez , Victor M. Eguiluz

Connectivity in temporal graphs relies on the notion of temporal paths, in which edges follow a chronological order (either strict or non-strict). In this work, we investigate the question of how to make a temporal graph connected. More…

Discrete Mathematics · Computer Science 2025-02-21 T. Bellitto , J. Bouton Popper , B. Escoffier

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

Machine Learning · Computer Science 2024-02-13 Lorenzo Giusti

Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different…

Machine Learning · Computer Science 2020-07-07 Vincent Froese , Brijnesh Jain , Rolf Niedermeier , Malte Renken

This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two…

Machine Learning · Computer Science 2023-03-29 Jianfei Gao , Bruno Ribeiro

Accessibility, defined as travel impedance between spatially dispersed opportunities for activity, is one of the main determinants of public transport use. In-depth understanding of its properties is crucial for optimal public transport…

Physics and Society · Physics 2026-03-24 Tina Šfiligoj , Aljoša Peperko , Oded Cats

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

Data Structures and Algorithms · Computer Science 2024-05-20 Davide Rucci

A temporal graph is a dynamic graph where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays…

Data Structures and Algorithms · Computer Science 2020-11-13 Argyrios Deligkas , Igor Potapov

We consider random-access networks with nodes representing transmitter-receiver pairs whose signals interfere with each other depending on their vicinity. Data packets arrive at the nodes over time and form queues. The nodes can be either…

Probability · Mathematics 2022-05-04 Matteo Sfragara

Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems TEMPORAL VERTEX COVER (or TVC) and SLIDING-WINDOW TEMPORAL VERTEX COVER(or $\Delta$-TVC for time-windows of a fixed-length $\Delta$)…

Data Structures and Algorithms · Computer Science 2024-03-22 Thekla Hamm , Nina Klobas , George B. Mertzios , Paul G. Spirakis

In directed graphs, a cycle can be seen as a structure that allows its vertices to loop back to themselves, or as a structure that allows pairs of vertices to reach each other through distinct paths. We extend these concepts to temporal…

Computational Complexity · Computer Science 2025-03-05 Davi de Andrade , Júlio Araújo , Allen Ibiapina , Andrea Marino , Jason Schoeters , Ana Silva

Here I present the present the first major result of a novel form of network analysis - a temporal interpretation. Treating numerical edges labels as the time at which an interaction occurs between the two vertices comprising that edge…

Combinatorics · Mathematics 2007-05-23 Benjamin de Bivort

We study the problem of patrolling the nodes of a network collaboratively by a team of mobile agents, such that each node of the network is visited by at least one agent once in every $I(n)$ time units, with the objective of minimizing the…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-08-14 Shantanu Das , Giuseppe Antonio Di Luna , Leszek A. Gasieniec

We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an…

Data Structures and Algorithms · Computer Science 2011-12-19 Fedor V. Fomin , Serge Gaspers , Petr Golovach , Karol Suchan , Stefan Szeider , Erik Jan van Leeuwen , Martin Vatshelle , Yngve Villanger

Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…

Social and Information Networks · Computer Science 2018-11-08 Shubham Gupta , Gaurav Sharma , Ambedkar Dukkipati

Dynamic graphs with ordered sequences of events between nodes are prevalent in real-world industrial applications such as e-commerce and social platforms. However, representation learning for dynamic graphs has posed great computational…

Machine Learning · Computer Science 2021-12-16 Xinshi Chen , Yan Zhu , Haowen Xu , Mengyang Liu , Liang Xiong , Muhan Zhang , Le Song

In the Travelling Salesman Problem, every vertex of an edge-weighted graph has to be visited by an agent who traverses the edges of the graph. In this problem, it is usually assumed that the costs of each edge are given in advance, making…

Data Structures and Algorithms · Computer Science 2025-01-31 Matthias Gehnen , Ralf Klasing , Émile Naquin

When the focus is on the relationships or interactions between entities, graphs offer an intuitive model for many real-world data. Such graphs are usually large and change over time, thus, requiring models and strategies that explore their…

Social and Information Networks · Computer Science 2024-02-07 Evangelia Tsoukanara , Georgia Koloniari , Evaggelia Pitoura , Peter Triantafillou

A temporal graph $\mathcal{G}=(G,\lambda)$ can be represented by an underlying graph $G=(V,E)$ together with a function $\lambda$ that assigns to each edge $e\in E$ the set of time steps during which $e$ is present. The reachability graph…

Computational Complexity · Computer Science 2025-03-21 Thomas Erlebach , Othon Michail , Nils Morawietz