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A (directed) temporal graph is a (directed) graph whose edges are available only at specific times during its (discretized) lifetime $\tau$. In this setting, we ask that walks respect the temporal aspect by defining $\textit{temporal…

Discrete Mathematics · Computer Science 2025-10-15 Allen Ibiapina , Raul Lopes , Andrea Marino , Ana Silva

Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…

Computational Complexity · Computer Science 2018-04-23 Hans-Joachim Böckenhauer , Janosch Fuchs , Walter Unger

In this paper we study two natural models of \textit{random temporal} graphs. In the first, the \textit{continuous} model, each edge $e$ is assigned $l_e$ labels, each drawn uniformly at random from $(0,1]$, where the numbers $l_e$ are…

Discrete Mathematics · Computer Science 2026-02-12 Henry Austin , George B. Mertzios , Paul G. Spirakis

A temporal graph is a graph whose edges appear at certain points in time. These graphs are temporally connected (in class TC) if all vertices can reach each other by temporal paths (traversing the edges in chronological order). Reachability…

Discrete Mathematics · Computer Science 2026-04-21 Arnaud Casteigts , Timothée Corsini , Nils Morawietz

Temporal network analysis and time evolution of network characteristics are powerful tools in describing the changing topology of dynamic networks. This paper uses such approaches to better visualize and provide analytical measures for the…

Multiagent Systems · Computer Science 2021-10-04 N. DiBrita , K. Eledlebi , H. Hildmann , L. Culley , A. F. Isakovic

Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…

Discrete Mathematics · Computer Science 2026-04-28 Jessica Enright , Samuel D. Hand , Laura Larios-Jones , Kitty Meeks

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…

Networking and Internet Architecture · Computer Science 2010-12-02 Prithwish Basu , Amotz Bar-Noy , Ram Ramanathan , Matthew P. Johnson

Shortcut sets are a vital instrument for reducing the diameter of a static graph and, consequently, its shortest path complexity, which is relevant in numerous subfields of graph theory. We explore the notion of shortcut sets in temporal…

Data Structures and Algorithms · Computer Science 2025-04-03 Gerome Quantmeyer

In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…

Data Structures and Algorithms · Computer Science 2025-04-24 Daniele Carnevale , Gianlorenzo D'Angelo , Martin Olsen

We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-07-19 Ioannis Lamprou , Russell Martin , Paul Spirakis

Learning in the space-time domain remains a very challenging problem in machine learning and computer vision. Current computational models for understanding spatio-temporal visual data are heavily rooted in the classical single-image based…

Computer Vision and Pattern Recognition · Computer Science 2020-05-26 Andrei Nicolicioiu , Iulia Duta , Marius Leordeanu

In this paper we study the problem of exploring a temporal graph (i.e. a graph that changes over time), in the fundamental case where the underlying static graph is a star. The aim of the exploration problem in a temporal star is to find a…

Computational Complexity · Computer Science 2018-05-15 Eleni C. Akrida , George B. Mertzios , Paul G. Spirakis

We study the computational complexity of determining structural properties of edge periodic temporal graphs (EPGs). EPGs are time-varying graphs that compactly represent periodic behavior of components of a dynamic network, for example,…

Computational Complexity · Computer Science 2022-03-16 Emmanuel Arrighi , Niels Grüttemeier , Nils Morawietz , Frank Sommer , Petra Wolf

Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…

Social and Information Networks · Computer Science 2011-02-04 Nicola Santoro , Walter Quattrociocchi , Paola Flocchini , Arnaud Casteigts , Frederic Amblard

Dynamic networks, a.k.a. graph streams, consist of a set of vertices and a collection of timestamped interaction events (i.e., temporal edges) between vertices. Temporal motifs are defined as classes of (small) isomorphic induced subgraphs…

Methodology · Statistics 2022-02-23 Xiaojing Zhu , Eric D. Kolaczyk

Modeling evolving interactions among entities is critical in many real-world tasks. For example, predicting driver maneuvers in traffic requires tracking how neighboring vehicles accelerate, brake, and change lanes relative to one another…

Artificial Intelligence · Computer Science 2025-09-23 Osama Mohammed , Jiaxin Pan , Mojtaba Nayyeri , Daniel Hernández , Steffen Staab

A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…

Computational Complexity · Computer Science 2024-07-01 Arnaud Casteigts , Nils Morawietz , Petra Wolf

Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…

Data Structures and Algorithms · Computer Science 2011-02-02 Oksana Denysyuk , Luis Rodrigues

Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as networks of telecommunication, neural signal processing, biochemical reactions and human…

Data Analysis, Statistics and Probability · Physics 2011-11-15 Lauri Kovanen , Márton Karsai , Kimmo Kaski , János Kertész , Jari Saramäki

Temporal graphs represent interactions between entities over the time. These interactions may be direct (a contact between two nodes at some time instant), or indirect, through sequences of contacts called temporal paths (journeys).…

Data Structures and Algorithms · Computer Science 2021-04-01 Luiz F. Afra Brito , Marcelo Albertini , Arnaud Casteigts , Bruno A. N. Travençolo
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