The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to compare the degree distribution of two given networks and extract the amount of similarity between the two distributions. In this paper, we propose a novel method for quantification of the degree distributions in complex networks. Based on this quantification method,a new distance function is also proposed for degree distributions, which captures the differences in the overall structure of the two given distributions. The proposed method is able to effectively compare networks even with different scales, and outperforms the state of the art methods considerably, with respect to the accuracy of the distance function.
Several network models have been proposed to explain the link structure observed in online social networks. This paper addresses the problem of choosing the model that best fits a given real-world network. We implement a model-selection method based on unsupervised learning. An alternating decision tree is trained using synthetic graphs generated according to each of the models under consideration. We use a broad array of features, with the aim of representing different structural aspects of the network. Features include the frequency counts of small subgraphs (graphlets) as well as features capturing the degree distribution and small-world property. Our method correctly classifies synthetic graphs, and is robust under perturbations of the graphs. We show that the graphlet counts alone are sufficient in separating the training data, indicating that graphlet counts are a good way of capturing network structure. We tested our approach on four Facebook graphs from various American universities. The models th...