Two-level relationships and scale-free networks

Through the distinction between “real” and “virtual” links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with preferential attachment, our procedure is both faster than a naïve implementation of the Barabási and Albert model and exhibits different clustering properties. The model is thoroughly studied numerically and suggests that reducing the set of partners a node can connect to is important in seizing the diversity of scale-free structures.