Related papers: Reachability in temporal graphs under perturbation
In this paper, we study temporal graphs arising from mobility models, where vertices correspond to agents moving in space and edges appear each time two agents meet. We propose a rather natural one-dimensional model. If each pair of agents…
Temporal graphs have edge sets that change over discrete time steps. Such graphs are temporally connected (TC) if all pairs of vertices can reach each other using paths that traverse the edges in a time-respecting way (temporal paths).…
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…
We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a…
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…
Temporal Graph Neural Network (TGNN) has been receiving a lot of attention recently due to its capability in modeling time-evolving graph-related tasks. Similar to Graph Neural Networks, it is also non-trivial to interpret predictions made…
Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
Temporal graphs are graphs where the topology and/or other properties of the graph change with time. They have been used to model applications with temporal information in various domains. Problems on static graphs become more challenging…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
Time-Basic Petri nets, is a powerful formalism for modeling real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We…
We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where…
In this work, we consider the following problem: given a digraph $G=(V,E)$, for each vertex $v$, we want to compute the number of vertices reachable from $v$. In other words, we want to compute the out-degree of each vertex in the…
We survey graph reachability indexing techniques for efficient processing of graph reachability queries in two types of popular graph models: plain graphs and edge-labeled graphs. Reachability queries are Boolean in nature, determining…
In dynamic graphs, edges may be added or deleted in each synchronous round. Various connectivity models exist based on constraints on these changes. One well-known model is the $T$-Interval Connectivity model, where the graph remains…
The Temporal Graph Exploration problem (TEXP) takes as input a temporal graph, i.e., a sequence of graphs $(G_i)_{i\in \mathbb{N}}$ on the same vertex set, and asks for a walk of shortest length visiting all vertices, where the $i$-th step…
Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary…
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…
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and…