Model Selection for Social Networks Using Graphlets

Abstract

Abstract. 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 that best fit these data are those that are based on the principle of preferential attachment.

Typical distances in a geometric model for complex networks

“…In [31], it was shown that the SPA model gave the best fit, in terms of graph structure, for a series of social networks derived from Facebook. In [32], some properties of common neighbors were used to explore the underlying geometry of the SPA model and quantify vertex similarity based on distance in the space.…”

Mining and Modeling Character Networks

“…An eigenvalue histogram is a histogram of the eigenvalues of the normalized Laplacian matrix, which all lie between 0 and 2, with equally spaced bins. These techniques are well established in model selection for various types of biological and social networks [6,14].…”

Noise-tolerant model selection and parameter estimation for complex networks

“…The set of considered network features is a source of diversity in the existing methods. Although some methods use both local and global network features in model selection [28,13], many existing methods are based on graphlet-counting features [29][30][31]25,26]. Graphlet counting is an inefficient approach, often accelerated by sampling [29] or approximation algorithms [32,29] which result in accuracy drops [28].…”

“…[28][29][30][31]). Additionally, the existing methods are sensitive to network perturbations, and their accuracy drops considerably if we inject noise to the network by making random changes in network edges.…”