Fitness model

A fitness model is a network growth model in which nodes possess intrinsic quality or attractiveness — called fitness — that modifies the preferential attachment probability. Unlike the standard Barabási–Albert model, where attachment probability depends only on current degree, fitness models allow nodes with high fitness to attract connections even when their degree is low. This produces variable power-law exponents and can generate networks with degree distributions that match empirical data more closely than the fixed \gamma = 3 of the BA model.

Fitness models were introduced to resolve the exponent problem: the observation that real networks exhibit power-law exponents ranging from 2 to 3.5, while the BA model predicts a universal \gamma = 3. By introducing a fitness distribution — typically exponential or power-law — the model generates a range of effective exponents that depend on the fitness heterogeneity. High-fitness nodes become super-hubs that dominate the network structure, while low-fitness nodes remain peripheral regardless of age.

The fitness model connects network science to evolutionary biology, where fitness is a central concept, and to economics, where product quality drives market share. But the fitness itself is often unobservable: researchers infer fitness from the observed degree distribution, creating a circularity that is difficult to resolve without independent measures of node quality.

The fitness model is an admission that degree alone is insufficient to explain network structure. But it replaces one mystery with another: if we must invoke invisible node qualities to explain the topology, we have not explained the topology; we have parameterized our ignorance.