Related papers: Testing Temporal Connectivity in Sparse Dynamic Gr…
We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…
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…
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…
In this paper we study flow problems on temporal networks, where edge capacities and travel times change over time. We consider a network with $n$ nodes and $m$ edges where the capacity and length of each edge is a piecewise constant…
Let $G$ be a directed graph with $n$ vertices and $m$ edges, embedded on a surface $S$, possibly with boundary, with first Betti number $\beta$. We consider the complexity of finding closed directed walks in $G$ that are either contractible…
Navigation on graphs is the problem how an agent walking on the graph can get from a source to a target with limited information about the graph. The information and the way to exploit it can vary. In this paper, we study navigation on…
Many tasks in graph machine learning, such as link prediction and node classification, are typically solved by using representation learning, in which each node or edge in the network is encoded via an embedding. Though there exists a lot…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
Temporal graph neural networks (TGNNs) have been widely used for modeling time-evolving graph-related tasks due to their ability to capture both graph topology dependency and non-linear temporal dynamic. The explanation of TGNNs is of vital…
Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
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…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…