2. Dynamic Models

A graph or hypergraph is a static representation of all possible interactions between nodes. However, due to these same interactions, the network topology evolves over time. The abundances of the chemical and/or molecular species they represent in nodes change over time and if they fall below a critical threshold, they cause the disappearance of any connected arches and then determine their reappearance if they return to exceed this critical threshold. The description of the dynamics of a network consists of a mathematical model often constituted by differential equations that express the speed of variation of the abundances of the biological entities represented by the nodes. The dynamics of a network can be deterministic, or stochastic or stochastic/deterministic hybrid. Depending on the nature of its determination, the dynamics is modelled by deterministic differential equations, stochastic differential equations, master equations, and in cases where the numerical solution of the latter is difficult to calculate, from stochastic simulation algorithms. In this chapter, we give an overview of the most used dynamic models for simulating the temporal evolution of a network.