Dynamic hierarchies in temporal directed networks

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 as an indicator for its relative importance in the network. In particular, it is among the most popular tools in social network analysis. In recent years, a growing number of real-world networks is modeled as temporal graphs, where we have ...

Community search is a well-studied problem which, given a static graph and a query set of vertices, requires to find a cohesive (or dense) subgraph containing the query vertices. In this paper we study the problem of community search in temporal dynamic networks. We adapt to the temporal setting the notion of \emph{network inefficiency} which is based on the pairwise shortest-path distance among all the vertices in a solution. For this purpose we define the notion of \emph{sh...

Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently led researchers to consider temporal versions of distance, connectivity, and related indicators), to the evolution of network properties over longer periods of time. This paper proposes a general approach to study that evolution for both ate...

Social network analysis tools can infer various attributes just by scrutinizing one's connections. Several researchers have studied the problem faced by an evader whose goal is to strategically rewire their social connections in order to mislead such tools, thereby concealing their private attributes. However, to date, this literature has only considered static networks, while neglecting the more general case of temporal networks, where the structure evolves over time. Driven...

Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we discuss fresh algorithmic views on temporal tree decompositions and temporal treewidth. We review and explain some of the recent work together with some encountered pitfalls, and we point out challenges for future research.

Network visualisation techniques are important tools for the exploratory analysis of complex systems. While these methods are regularly applied to visualise data on complex networks, we increasingly have access to time series data that can be modelled as temporal networks or dynamic graphs. In dynamic graphs, the temporal ordering of time-stamped edges determines the causal topology of a system, i.e., which nodes can, directly and indirectly, influence each other via a so-cal...

Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in which links occur in real-world temporal networks affects causality structures and thus the evolution of dynamical processes, and ii) higher-order aggregate representations of temporal networks can be used to analytically study the effect of th...

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. Nevertheless, in the model for temporal networks of [Kempe et al., JCSS, 2002], the individual time-labeled edges remain undirected: an edge $e=\{u,v\}$ with time-label $t$ specifies that "$u$ communicates with $v$ at time $t$". This is a symme...

We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that information does not necessarily spread on shortest paths but on temporal random walks that satisfy the time constraints of the network. We show that temporal walk centrality can identify nodes playing central roles in dissemination processes...

We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of data by using existing graph algorithms (such as shortest-path), with no need for data-driven simulations. We also present a number of metrics that can be used to study and explore temporal graphs. Finally, we use temporal graphs to analyse r...