Time-varying network

A temporal network, also known as a time-varying network, is a network whose links are active only at certain points in time. 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. A temporal network, also known as a time-varying network, is a network whose links are active only at certain points in time. 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. Information spreads over both networks, and some computer viruses spread over the second. Networks of physical proximity, encoding who encounters whom and when, can be represented as time-varying networks. 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.Neural networks and brain networks can be represented as time-varying networks since the activation of neurons are time-correlated. Time-varying networks are characterized by intermittent activation at the scale of individual links. This is in contrast to various models of network evolution, which may include an overall time dependence at the scale of the network as a whole. Time-varying networks are inherently dynamic, and used for modeling spreading processes on networks. Whether using time-varying networks will be worth the added complexity depends on the relative time scales in question. Time-varying networks are most useful in describing systems where the spreading process on a network and the network itself evolve at similar timescales. Let the characteristic timescale for the evolution of the network be t N {displaystyle t_{N}} , and the characteristic timescale for the evolution of the spreading process be t P {displaystyle t_{P}} . A process on a network will fall into one of three categories: The flow of data over the internet is an example for the first case, where the network changes very little in the fraction of a second it takes for a network packet to traverse it. 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. 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. There are three common representations for time-varying network data. The measures used to characterize static networks are not immediately transferable to time-varying networks. See Path, Connectedness, Distance, Centrality. However, these network concepts have been adapted to apply to time-varying networks. 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. Like in a directed graph, a path from i {displaystyle i} to j {displaystyle j} does not mean there is a path from j {displaystyle j} to i {displaystyle i} . In contrast to paths in static and evolving networks, however, time respecting paths are also non-transitive. That is to say, just because there is a path from i {displaystyle i} to j {displaystyle j} and from j {displaystyle j} to k {displaystyle k} does not mean that there is a path from i {displaystyle i} to k {displaystyle k} . Furthermore, time respecting paths are themselves time-varying, and are only valid paths during a specific time interval.