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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 graphs are a class of graphs defined by a constant set of vertices and a changing set of edges, each of which is known as a timestep. These graphs are well motivated in modelling real-world networks, where connections may change…

Data Structures and Algorithms · Computer Science 2025-05-21 Duncan Adamson

Deep graph clustering has recently received significant attention due to its ability to enhance the representation learning capabilities of models in unsupervised scenarios. Nevertheless, deep clustering for temporal graphs, which could…

Machine Learning · Computer Science 2024-04-12 Meng Liu , Yue Liu , Ke Liang , Wenxuan Tu , Siwei Wang , Sihang Zhou , Xinwang Liu

Temporal knowledge graphs (TKGs) inherently reflect the transient nature of real-world knowledge, as opposed to static knowledge graphs. Naturally, automatic TKG completion has drawn much research interests for a more realistic modeling of…

Machine Learning · Computer Science 2020-12-22 Jaehun Jung , Jinhong Jung , U Kang

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…

Adaptation and Self-Organizing Systems · Physics 2012-10-10 Petter Holme , Jari Saramäki

Representing the movements of objects (trips) over a network in a compact way while retaining the capability of exploiting such data effectively is an important challenge of real applications. We present a new Compact Trip Representation…

Data Structures and Algorithms · Computer Science 2019-01-01 Nieves R. Brisaboa , Antonio Fariña , Daniil Galaktionov , M. Andrea Rodriguez

In a temporal forest each edge has an associated set of time labels that specify the time instants in which the edges are available. A temporal path from vertex $u$ to vertex $v$ in the forest is a selection of a label for each edge in the…

Data Structures and Algorithms · Computer Science 2024-09-30 Davide Bilò , Luciano Gualà , Stefano Leucci , Guido Proietti , Alessandro Straziota

We study a family of reachability problems under waiting-time restrictions in temporal and vertex-colored temporal graphs. Given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via…

Data Structures and Algorithms · Computer Science 2024-12-04 Suhas Thejaswi , Juho Lauri , Aristides Gionis

With the proliferation of temporal graph data, there is a growing demand for analyzing information propagation patterns during graph evolution. Existing graph analysis systems, mostly based on static snapshots, struggle to effectively…

Databases · Computer Science 2025-12-30 Jiacheng Ding , Cong Guo , Xiaofei Zhang

A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…

Combinatorics · Mathematics 2023-03-01 Isnard Lopes Costa , Raul Lopes , Andrea Marino , Ana Silva

Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…

Data Structures and Algorithms · Computer Science 2022-04-27 Luiz F. A. Brito , Bruno A. N. Travençolo , Marcelo K. Albertini

Dynamic temporal graphs represent evolving relations between entities, e.g. interactions between social network users or infection spreading. We propose an extension of graph echo state networks for the efficient processing of dynamic…

Machine Learning · Computer Science 2022-10-31 Domenico Tortorella , Alessio Micheli

This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…

Computational Geometry · Computer Science 2023-08-15 Audun Myers , David Muñoz , Firas Khasawneh , Elizabeth Munch

Conventional static knowledge graphs model entities in relational data as nodes, connected by edges of specific relation types. However, information and knowledge evolve continuously, and temporal dynamics emerge, which are expected to…

Machine Learning · Computer Science 2022-03-10 Yushan Liu , Yunpu Ma , Marcel Hildebrandt , Mitchell Joblin , Volker Tresp

Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and…

Logic in Computer Science · Computer Science 2018-04-25 Samir Datta , Anish Mukherjee , Nils Vortmeier , Thomas Zeume

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

Temporal knowledge graph completion (TKGC) aims to fill in missing facts within a given temporal knowledge graph at a specific time. Existing methods, operating in real or complex spaces, have demonstrated promising performance in this…

Machine Learning · Computer Science 2024-03-06 Li Cai , Xin Mao , Zhihong Wang , Shangqing Zhao , Yuhao Zhou , Changxu Wu , Man Lan

What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…

Category Theory · Mathematics 2026-04-22 Benjamin Merlin Bumpus , James Fairbanks , Martti Karvonen , Wilmer Leal , Frédéric Simard

Deep learning-based predictive models, leveraging Electronic Health Records (EHR), are receiving increasing attention in healthcare. An effective representation of a patient's EHR should hierarchically encompass both the temporal…

Machine Learning · Computer Science 2024-05-08 Jiayuan Chen , Changchang Yin , Yuanlong Wang , Ping Zhang

An accessibility graph of a network contains a link, wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding…

Physics and Society · Physics 2012-10-09 Hartmut H K Lentz , Thomas Selhorst , Igor M Sokolov