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Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths…

Data Structures and Algorithms · Computer Science 2018-07-26 Philipp Zschoche , Till Fluschnik , Hendrik Molter , Rolf Niedermeier

The betweenness centrality of a graph vertex measures how often this vertex is visited on shortest paths between other vertices of the graph. In the analysis of many real-world graphs or networks, betweenness centrality of a vertex is used…

Data Structures and Algorithms · Computer Science 2024-05-15 Sebastian Buß , Hendrik Molter , Rolf Niedermeier , Maciej Rymar

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

Reasoning about graphs evolving over time is a challenging concept in many domains, such as bioinformatics, physics, and social networks. We consider a common case in which edges can be short term interactions (e.g., messaging) or long term…

Machine Learning · Statistics 2020-06-22 Boris Knyazev , Carolyn Augusta , Graham W. Taylor

Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…

Machine Learning · Computer Science 2022-08-26 Shubham Gupta , Srikanta Bedathur

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…

Machine Learning · Computer Science 2024-09-11 Alessio Gravina , Daniele Zambon , Davide Bacciu , Cesare Alippi

Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring…

Machine Learning · Computer Science 2023-10-31 Jialin Chen , Rex Ying

We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time…

Probability · Mathematics 2023-06-21 Nicolas Broutin , Nina Kamčev , Gabor Lugosi

Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…

Machine Learning · Computer Science 2023-11-02 Yu Yang , Hongzhi Yin , Jiannong Cao , Tong Chen , Quoc Viet Hung Nguyen , Xiaofang Zhou , Lei Chen

Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…

Discrete Mathematics · Computer Science 2025-05-23 Jessica Enright , Laura Larios-Jones , Kitty Meeks , William Pettersson

Many real-world networks, such as transportation or trade networks, are dynamic in the sense that the edge set may change over time, but these changes are known in advance. This behavior is captured by the temporal graphs model, which has…

We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…

Data Structures and Algorithms · Computer Science 2021-05-25 Nina Klobas , George B. Mertzios , Hendrik Molter , Rolf Niedermeier , Philipp Zschoche

Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timings of node and link activations. In this paper, we set to explore the latter by using greedy walks as probes of…

Physics and Society · Physics 2016-01-20 Jari Saramaki , Petter Holme

Networks are a fundamental and flexible way of representing various complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their…

Social and Information Networks · Computer Science 2020-08-07 Sumit Purohit , Lawrence B. Holder , George Chin

A temporal graph is a graph in which connections between vertices are active at specific times, and such temporal information leads to completely new patterns and knowledge that are not present in a non-temporal graph. In this paper, we…

Data Structures and Algorithms · Computer Science 2014-01-10 Silu Huang , James Cheng , Huanhuan Wu

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

In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…

Data Structures and Algorithms · Computer Science 2025-10-03 Justine Cauvi , Nils Morawietz , Laurent Viennot

With the growing amount of available temporal real-world network data, an important question is how to efficiently study these data. One can simply model a temporal network as either a single aggregate static network, or as a series of…

Social and Information Networks · Computer Science 2014-12-15 Yuriy Hulovatyy , Huili Chen , Tijana Milenkovic

This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…

Methodology · Statistics 2022-07-07 Maria Suveges , Sofia C. Olhede

In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in…

Data Structures and Algorithms · Computer Science 2024-05-02 Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis