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We consider two variants, (s,z,l)-Temporal Separator and (s,z,l)-Temporal Cut, respectively, of the vertex separator and the edge cut problem in temporal graphs. The goal is to remove the minimum number of vertices (temporal edges,…
Betweenness centrality has been extensively studied since its introduction in 1977 as a measure of node importance in graphs. This measure has found use in various applications and has been extended to temporal graphs with time-labeled…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…
Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems TEMPORAL VERTEX COVER (or TVC) and SLIDING-WINDOW TEMPORAL VERTEX COVER(or $\Delta$-TVC for time-windows of a fixed-length $\Delta$)…
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different…
We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an…
Let $\mbox{interval} + k v$, $\mbox{interval} + k e$, and $\mbox{interval} - k e$ denote the classes of graphs that can be obtained from some interval graph by adding $k$ vertices, adding $k$ edges, and deleting $k$ edges, respectively.…
For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection…
Real-world graphs often contain spatio-temporal information and evolve over time. Compared with static graphs, spatio-temporal graphs have very different characteristics, presenting more significant challenges in data volume, data velocity,…
The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented levels of details and scale. Wearable sensors are opening up a new window on human mobility and proximity at the…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
Temporal information is increasingly available as part of large network data sets. This information reveals sequences of link activations between network entities, which can expose underlying processes in the data. Examples include the…
We discuss the complexity of path enumeration and counting in weighted temporal graphs. In a weighted temporal graph, each edge has an availability time, a traversal time and some real cost. We introduce two bicriteria temporal min-cost…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…
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…
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…
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…
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…
In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two…
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…