Router BarabasiAlbert (Barabási-Albert model)

BRITE provides a RouterBarabasiAlbert model deriving from the Model class. It is called RouterBarabasiAlbert because it implements a model proposed by Barabási and Albert [2]. This model suggests two possible causes for the emergence of a power law in the frequency of outdegrees in network topologies: incremental growth and preferential connectivity. Incremental growth refers to growing networks that are formed by the continual addition of new nodes, and thus the gradual increase in the size of the network. Preferential connectivity refers to the tendency of a new node to connect to existing nodes that are highly connected or popular.

RouterBarabasiAlbert interconnects the nodes according to the incremental growth approach. When a node $i$ joins the network, the probability that it connects to a node $j$ already belonging to the network is given by:

$$P(i,j) = \frac{d_{j}}{\sum_{k \in V}{d_{k}}}$$ (2)

where $d_{j}$ is the degree of the target node, $V$ is the set of nodes that have joined the network and $\sum_{k \in V}{d_{k}}$ is the sum of outdegrees of all nodes that previously joined the network.