Activitydriven

Activitydriven is a framework used to model and analyze time-varying networks in which the formation of connections is governed by the intrinsic activity of each node. It is commonly applied in network science and epidemiology to study how evolving contact patterns affect dynamical processes such as diffusion, information spread, and contagion. The approach emphasizes that individual activity levels drive interactions over time.

In the standard activity-driven model, each node i is assigned an activity rate a_i drawn from a distribution F(a). Time is discrete. At each time step, node i becomes active with probability proportional to a_i; when active, it creates a fixed number m of edges to other nodes chosen uniformly at random, and these edges exist only for that time step. After the step, all links disappear, producing a sequence of instantaneous networks. The aggregate of these networks over time captures the evolving structure while maintaining analytical tractability.

Extensions and variants include memory effects (active nodes preferentially reconnect to previous partners), the introduction of community structure and degree correlations, directed or weighted edges, and correlations between activity and other node attributes. Some models incorporate persistent links or time-varying activity rates to better reflect real-world patterns, balancing simplicity with realism.

Applications of activity-driven models center on understanding how heterogeneity in activity influences spreading dynamics, such as epidemic thresholds, outbreak sizes, and diffusion speed. The framework is valued for its simplicity, scalability, and ability to reproduce key features of temporal networks, though it omits geography, stable ties, and complex social preferences unless extended. See also temporal networks; foundational work by Perra, Gonçalves, Pastor-Satorras, and Vespignani (2012).