BarabásiAlbertnätverk

Barabási-Albert networks, often abbreviated as BA networks, are a type of generative model for random networks. They are characterized by two key mechanisms: growth and preferential attachment. Growth means that the network starts with a small number of nodes and new nodes are added over time. Preferential attachment means that as new nodes are added, they are more likely to connect to existing nodes that already have a high degree (i.e., many connections). This mechanism is often described as "the rich get richer."

The Barabási-Albert model was introduced by Albert-László Barabási and Réka Albert in 1999. It was developed to explain the observed properties of many real-world networks, such as the internet, citation networks, and social networks, which often exhibit a scale-free degree distribution. This means that while most nodes have only a few connections, a small number of nodes (hubs) have a disproportionately large number of connections. This contrasts with simpler random network models like the Erdős–Rényi model, which typically have a Poisson degree distribution.

The BA model is able to reproduce this scale-free property. The growing nature of the network allows it to evolve over time, while the preferential attachment mechanism ensures that hubs emerge and persist. The degree distribution of a BA network follows a power law, meaning that the probability of a node having a degree k is proportional to k raised to some negative exponent. This type of distribution is characteristic of many complex systems and has significant implications for how information spreads or how resilient the network is to failures.