Step-by-Step Random Walk Network with Power-Law Clique-Degree Distribution

We propose a simple mechanism for generating scale-free networks with degree exponent γ= 3, where the new node is connected to the existing nodes by step-by-step random walk. It is found that the clique-degree distribution based on our model obeys a power-law form, which is in agreement with the recently empirical evidences. In addition, our model displays the small-world effect and the hierarchical structure.