In complex network theory, the fitness model is a model of the evolution of a network: how the links between nodes change over time depends on the fitness of nodes.
It has been used to model the network structure of the World Wide Web.
The model is based on the idea of fitness, an inherent competitive factor that nodes may have, capable of affecting the network's evolution.
In that sense, not all nodes are identical to each other, and they claim their degree increase according to the fitness they possess every time.
The fitness factors of all the nodes composing the network may form a distribution ρ(η) characteristic of the system been studied.
The fitness parameter is time-independent and is multiplicative to the probability.
are distributed as a power law, then also the node degree does.
Such model has been successfully applied to describe trade between nations by using GDP as fitness for the various nodes
In a PNAS article,[6] Kong et al. extended the fitness model to include random node deletion, a common phenomena in the Web.
When the deletion rate of the web pages are accounted for, they found that the overall fitness distribution is exponential.
Nonetheless, even this small variance in the fitness is amplified through the preferential attachment mechanism, leading to a heavy-tailed distribution of incoming links on the Web.