Growing scale-free networks with tunable distributions of triad motifs

• A model to grow scale-free networks with tunable motif distributions.
• A combined operation of preferential attachment and triad motif seeding.
• Networks with adjustable distributions of the local triad motifs.
• Networks with “scale-free”, “small-world” and high clustering features.

Network motifs are local structural patterns and elementary functional units of complex networks in real world, which can have significant impacts on the global behavior of these systems. Many models are able to reproduce complex networks mimicking a series of global features of real systems, however the local features such as motifs in real networks have not been well represented. We propose a model to grow scale-free networks with tunable motif distributions through a combined operation of preferential attachment and triad motif seeding steps. Numerical experiments show that the constructed networks have adjustable distributions of the local triad motifs, meanwhile preserving the global features of power-law distributions of node degree, short average path lengths of nodes, and highly clustered structures.