Effect of attachment strategies on bipartite networks

Bipartite systems show remarkable variations in their topological asymptotic properties, e. g., in their degree distribution. Such variations depend on the underlying growth dynamics. A scenario of particular importance is when the two partitions of the bipartite structure do not grow at an equal rate. Here, we focus on the case where one of the partitions can be assumed to be fixed while the other partition grows in time as observed in the codon-gene or alphabet-word network. We show that subtle changes in growth dynamics, particularly in the attachment kernel, can lead to drastic changes of the emergent topological properties. We present a detail analysis of various growth strategies, including sequential and parallel addition of nodes, as well as with and without replacement attachment kernels. Analytical results have been compared with stochastic simulations as well as with real systems showing in all cases an excellent agreement.