Measuring realism of social network models using network motifs

Social networks analysis is an emergent field of science which aims to study, model, and predict processes and relationships found in nature through the usage of graphs. To that end, since the discovery of fundamental properties like small-world effect and preferential attachment, the last decade has witnessed a boom of more fine-tuned, more complex social network models. Despite of a plethora of existing models for social evolution and behavior, none have come close enough to model the real world societies we live in. This paper proposes to study nine of the most relevant state-of-the-art network models and classify them based on their real-world fidelity. As such, we introduce three empirical datasets: Facebook, Google Plus and Twitter online networks, and use them as references for computing realism. As a mathematical tool, we use network motifs and compute the similarity using the referenced fidelity metric φ. Our results showcase a new perspective on how one can compare and assess synthetic network models, and we find that some networks are indeed better substitutes for real-world networks (e.g. cellular networks have a realism of 68%), while others are weak substitutes (e.g. scale-free networks have a realism of 29%).