Graph Metrics for Temporal Networks

  title={Graph Metrics for Temporal Networks},
  author={Vincenzo Nicosia and John Kit Tang and Cecilia Mascolo and Mirco Musolesi and Giovanni Russo and Vito Latora},
Temporal networks, i.e., networks in which the interactions among a set of elementary units change over time, can be modelled in terms of time-varying graphs, which are time-ordered sequences of graphs over a set of nodes. In such graphs, the concepts of node adjacency and reachability crucially depend on the exact temporal ordering of the links. Consequently, all the concepts and metrics proposed and used for the characterisation of static complex networks have to be redefined or appropriately… 
Algorithmic Aspects of Temporal Betweenness
This work provides a systematic study of temporal betweenness variants based on various concepts of optimal temporal paths both on a theoretical and empirical level.
Coverage centralities for temporal networks
This paper defines two centrality measures of a temporal vertex based on the fastest temporal paths which use the temporal vertex, and reveals that distributions of these centrality values of real-world temporal networks are heterogeneous.
Time evolution of the importance of nodes in dynamic networks
This paper proposes temporal extensions of notions of centrality, which take into account the paths existing at any given time, in order to study the time evolution of nodes' importance in dynamic networks and shows that the importance of nodes does indeed vary greatly with time.
Stream graphs and link streams for the modeling of interactions over time
This paper generalizes graph concepts to cope with both intrinsically temporal and structural nature of interactions, and obtains a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations.
The Complexity of Transitively Orienting Temporal Graphs
This paper introduces the fundamental notion of a temporal transitive orientation and systematically investigates its algorithmic behavior in various situations and proves that, surprisingly, it is NP-hard to recognize whether a given temporal graph G is transitively orientable.
Temporal Walk Centrality: Ranking Nodes in Evolving Networks
It is shown that temporal walk centrality can identify nodes playing central roles in dissemination processes that might not be detected by related betweenness concepts and other common static and temporal centrality measures.
Centrality Metrics in Dynamic Networks: A Comparison Study
A method recently introduced to three existing methods for evaluating the importance of nodes in static networks is compared, and it is shown that in some cases it might be meaningless to try to identify nodes that are globally important.
Spatio-temporal networks: reachability, centrality and robustness
A model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded is proposed.
Clone temporal centrality measures for incomplete sequences of graph snapshots
This work suggests to use clone temporal centrality measures in incomplete graph sequences settings to improve the detection rate of important vertices in dynamic networks compared to approaches that do not compensate for incompleteness.
Spatio-Temporal Complex Networks: Reachability, Centrality, and Robustness
This paper proposes a model of spatio-temporal paths in time-varying spatially embedded networks that captures the property that, in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded.


Components in time-varying graphs
The notion of connectedness, and the definitions of node and graph components, are extended to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes.
Path lengths, correlations, and centrality in temporal networks
  • R. Pan, J. Saramäki
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
Differences between static and temporal properties are further highlighted in studies of the temporal closeness centrality, and correlations and heterogeneities in the underlying event sequences affect temporal path lengths, increasing temporal distances in communication networks and decreasing them in the air transport network.
Applications of Temporal Graph Metrics to Real-World Networks
This work analyses the roles of key individuals of a corporate network ranked according to temporal centrality within the context of a bankruptcy scandal, and demonstrates that temporal metrics provide a more accurate and effective analysis of real-world networks compared to their static counterparts.
Characterising temporal distance and reachability in mobile and online social networks
New temporal distance metrics to quantify and compare the speed (delay) of information diffusion processes taking into account the evolution of a network from a global view are proposed and shown how these metrics are able to capture the temporal characteristics of time-varying graphs.
Temporal Networks
The structure of information pathways in a social communication network
This work forms a temporal notion of "distance" in the underlying social network by measuring the minimum time required for information to spread from one node to another - a concept that draws on the notion of vector-clocks from the study of distributed computing systems.
Analysing information flows and key mediators through temporal centrality metrics
It is argued that dynamically evolving network topologies are inherent in many systems, including real online social and technological networks: fortunately the nature of these systems is such that they allow the gathering of large quantities of finegrained temporal data on interactions amongst the network members.
Small-world behavior in time-varying graphs.
This work defines as temporal small world a time-varying graph in which the links are highly clustered in time, yet the nodes are at small average temporal distances, and explores the small-world behavior in synthetic time- varying networks of mobile agents and in real social and biological time-Varying systems.
Microdynamics in stationary complex networks
A model of dynamical networks is proposed, inspired from previous studies on firm growth, which reproduces most of the empirical observations both for the stationary statistical distributions and for the dynamical properties.
Temporal motifs in time-dependent networks
The framework of temporal motifs is introduced to study the mesoscale topological–temporal structure of temporal networks in which the events of nodes do not overlap in time and a mapping from event sequences to coloured directed graphs is provided that enables an efficient algorithm for identifying temporal motifS.