Activity-driven model

In network science, the activity-driven model is a temporal network model in which each node has a randomly-assigned "activity potential", which governs how it links to other nodes over time. Each node j (out of N total) has its activity potential x_i drawn from a given distribution F(x) . A sequence of timesteps unfolds, and in each timestep each node j forms ties to m random other nodes at rate a_i=\eta x_i (more precisely, it does so with probability a_i \, \Delta t per timestep). All links are then deleted after each timestep. Properties of time-aggregated network snapshots are able to be studied in terms of F(x) . For example, since each node j after T timesteps will have on average m\eta x_i T outgoing links, the degree distribution after T timesteps in the time-aggregated network will be related to the activity-potential distribution by : P_T(k) \propto F\left(\frac{k}{m\eta T}\right).…

In network science, the activity-driven model is a temporal network model in which each node has a randomly-assigned "activity potential", which governs how it links to other nodes over time. Each node j (out of N total) has its activity potential x_i drawn from a given distribution F(x) . A sequence of timesteps unfolds, and in each timestep each node j forms ties to m random other nodes at rate a_i=\eta x_i (more precisely, it does so with probability a_i \, \Delta t per timestep). All links are then deleted after each timestep. Properties of time-aggregated network snapshots are able to be studied in terms of F(x) . For example, since each node j after T timesteps will have on average m\eta x_i T outgoing links, the degree distribution after T timesteps in the time-aggregated network will be related to the activity-potential distribution by P_T(k) \propto F\left(\frac{k}{m\eta T}\right). Spreading behavior according to the SIS epidemic model was investigated on activity-driven networks, and the following condition was derived for large-scale outbreaks to be possible: \frac{\beta}{\lambda} > \frac{2\langle a\rangle}{\langle a\rangle + \sqrt{\langle a^2\rangle}}, where \beta is the per-contact transmission probability, \lambda is the per-timestep recovery probability, and ( \langle a\rangle , \langle a^2\rangle ) are the first and second moments of the random activity-rate a_j .

Text derived from https://en.wikipedia.org/w/index.php?oldid=1369795547 under CC BY-SA 4.0; modifications have been made.