Generating Scale-Free Caterpillar and Series-Parallel Networks

Generating synthetic networks with special properties is an important topic of research in network science.Generative algorithms enable researchers to replicate complex network structures, facilitating in-depth analysis and validate different algorithms.One such important type of networks is a scale-free network.Many real networks, irrespective of their discipline, function or scope follow the scale free property.In a scale-free network the vertex connectivity follows a power-law distribution where the probability of a vertex having degree is proportional to - with 2 < < 3. Starting from Albert-Barabasi model, numerous models have been developed to generate scale-free networks.But generative models for scale-free networks of desired graph (network) classes has been a key scope of work.In this paper, we focus on two special graph classes called caterpillars and series-parallel networks.We characterize the value of required for constructing a scale-free caterpillar network and provide an () algorithm for generating scale-free caterpillar networks of vertices.We also provide an () algorithm for generating scale-free series-parallel networks of edges.