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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

A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first $\Delta$ time steps, and then it reappears recurrently every $\Delta$ time steps, where $\Delta$ is a given period length.…

Data Structures and Algorithms · Computer Science 2025-04-22 George B. Mertzios , Hendrik Molter , Nils Morawietz , Paul G. Spirakis

A graph is temporally connected if there exists a strict temporal path, i.e. a path whose edges have strictly increasing labels, from every vertex $u$ to every other vertex $v$. In this paper we study temporal design problems for undirected…

Data Structures and Algorithms · Computer Science 2022-05-03 Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis

A temporal graph is a graph in which edges are assigned a time label. Two nodes u and v of a temporal graph are connected one to the other if there exists a path from u to v with increasing edge time labels. We consider the problem of…

Data Structures and Algorithms · Computer Science 2023-04-04 Alkida Balliu , Filippo Brunelli , Pierluigi Crescenzi , Dennis Olivetti , Laurent Viennot

We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be…

Discrete Mathematics · Computer Science 2025-01-22 Filippo Brunelli , Pierluigi Crescenzi , Laurent Viennot

We study the design of small cost temporally connected graphs, under various constraints. We mainly consider undirected graphs of $n$ vertices, where each edge has an associated set of discrete availability instances (labels). A journey…

Discrete Mathematics · Computer Science 2016-07-07 Eleni C. Akrida , Leszek Gasieniec , George B. Mertzios , Paul G. Spirakis

In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…

Data Structures and Algorithms · Computer Science 2023-01-31 Filippo Brunelli , Laurent Viennot

In this work we consider temporal graphs, i.e. graphs, each edge of which is assigned a set of discrete time-labels drawn from a set of integers. The labels of an edge indicate the discrete moments in time at which the edge is available. We…

Data Structures and Algorithms · Computer Science 2013-10-30 Paul G. Spirakis , Eleni Ch. Akrida

A temporal graph can be represented by a graph with an edge labelling, such that an edge is present in the network if and only if the edge is assigned the corresponding time label. A journey is a labelled path in a temporal graph such that…

Computational Complexity · Computer Science 2023-12-13 Esteban Christiann , Eric Sanlaville , Jason Schoeters

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

Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to…

Machine Learning · Computer Science 2022-10-04 Sudhanshu Chanpuriya , Ryan A. Rossi , Sungchul Kim , Tong Yu , Jane Hoffswell , Nedim Lipka , Shunan Guo , Cameron Musco

In a wide range of complex networks, the links between the nodes are temporal and may sporadically appear and disappear. This temporality is fundamental to analyze the formation of paths within such networks. Moreover, the presence of the…

Physics and Society · Physics 2017-09-20 Shahriar Etemadi Tajbakhsh , Justin P. Coon , David E. Simmons

Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs…

Data Structures and Algorithms · Computer Science 2018-01-25 Patrick Mackey , Katherine Porterfield , Erin Fitzhenry , Sutanay Choudhury , George Chin

A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed…

Discrete Mathematics · Computer Science 2015-03-03 Othon Michail

Logistics and transportation networks require a large amount of resources to realize necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connections…

Social and Information Networks · Computer Science 2024-09-02 Argyrios Deligkas , Michelle Döring , Eduard Eiben , Tiger-Lily Goldsmith , George Skretas , Georg Tennigkeit

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…

Discrete Mathematics · Computer Science 2020-09-30 George B. Mertzios , Hendrik Molter , Rolf Niedermeier , Viktor Zamaraev , Philipp Zschoche

We introduce the \emph{temporal graphlet kernel} for classifying dissemination processes in labeled temporal graphs. Such dissemination processes can be spreading (fake) news, infectious diseases, or computer viruses in dynamic networks.…

Social and Information Networks · Computer Science 2022-09-16 Lutz Oettershagen , Nils M. Kriege , Claude Jordan , Petra Mutzel

In a temporal network with discrete time-labels on its edges, entities and information can only ``flow'' along sequences of edges whose time-labels are non-decreasing (resp. increasing), i.e. along temporal (resp. strict temporal) paths.…

Data Structures and Algorithms · Computer Science 2025-01-29 George B. Mertzios , Hendrik Molter , Malte Renken , Paul G. Spirakis , Philipp Zschoche

Temporal networks consist of timestamped directed interactions that may appear continuously in time, yet few studies have directly tackled the continuous-time modeling of networks. Here, we introduce a maximum-entropy approach to temporal…

Social and Information Networks · Computer Science 2026-04-16 Paolo Barucca

Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between…

Computer Science and Game Theory · Computer Science 2023-05-23 Davide Bilò , Sarel Cohen , Tobias Friedrich , Hans Gawendowicz , Nicolas Klodt , Pascal Lenzner , George Skretas
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