Each link carries information on when it is active, along with other possible characteristics such as a weight.
Time-varying networks are of particular relevance to spreading processes, like the spread of information and disease, since each link is a contact opportunity and the time ordering of contacts is included.
Examples of time-varying networks include communication networks where each link is relatively short or instantaneous, such as phone calls or e-mails.
[3] Some diseases, such as airborne pathogens, spread through physical proximity.
Real-world data on time resolved physical proximity networks has been used to improve epidemic modeling.
[5] Time-varying networks are characterized by intermittent activation at the scale of individual links.
Whether using time-varying networks will be worth the added complexity depends on the relative time scales in question.
, and the characteristic timescale for the evolution of the spreading process be
[7] The spread of sexually transmitted diseases is an example of the second, where the prevalence of the disease spreads in direct correlation to the rate of evolution of the sexual contact network itself.
[8] Behavioral contagion is an example of the third case, where behaviors spread through a population over the combined network of many day-to-day social interactions.
[9] There are three common representations for time-varying network data.
Time respecting paths are the sequences of links that can be traversed in a time-varying network under the constraint that the next link to be traversed is activated at some point after the current one.
The reachability ratio can be defined as the average over all nodes
[12] Connectedness of an entire network is less conclusively defined, although some have been proposed.
A component may be defined as strongly connected if there is a directed time respecting path connecting all nodes in the component in both directions.
A component may be defined as weakly connected if there is an undirected time respecting path connecting all nodes in the component in both directions.
Causal fidelity quantifies the goodness of the static approximation of a temporal network.
Such a static approximation is generated by aggregating the edges of a temporal network over time.
The idea of causal fidelity is to compare the number of paths between all node pairs in the temporal network
means that the considered temporal network is well approximated by its static (aggregated) counterpart.
, then most node pairs that are reachable in the static representation are not connected by time respecting paths in the temporal network.
In a time-varying network any time respecting path has a duration, namely the time it takes to follow that path.
The fastest such path between two nodes is the latency, note that it is also dependent on the start time.
Measuring centrality on time-varying networks involves a straightforward replacement of distance with latency.
It is possible to extract recurring and persistent patterns of contact from time-varying data in many ways.
The distribution of inter-event times of a growing number of important, real-world, time-varying networks have been found to be bursty, meaning inter-event times are very heterogeneous – they have a heavy-tailed distribution.
[20] Burstiness of inter-event times can dramatically slow spreading processes on networks,[21] which has implications for the spread of disease, information, ideas, and computer viruses.
[22] Real-world time-varying networks may thus promote spreading processes despite having a bursty inter-event time distribution.
[23] Burstiness as an empirical quantity can be calculated for any sequence of inter-event times,
, by comparing the sequence to one generated by a Poisson process.