We propose methods on two fundamental graph theoretic problems: (1) network comparison, and (2) network modelling. Our methods are applied to five real-world network types, with an emphasis on world trade networks (WTNs), which we choose due to the world's current economic crisis.

Finding topological similarities of complex networks is computationally intractable due to NP-Completeness of the subgraph isomorphism problem. Hence, simple heuristics have been used for this purpose. The most sophisticated heuristics are based on graph spectra and small subnetworks including graphlets. Among these, graphlets are preferred since spectra do not provide a direct real-world interpretation of network structure. However, current graphlet-based techniques can be improved. We improve graphlet-based heuristics by defining a new network topology descriptor, Graphlet Correlation Matrix (GCM), which eliminates all redundancies and quantifies the dependencies in graphlet properties. Then, we introduce a new network distance measure, Graphlet Correlation Distance (GCD), that compares GCMs of two networks. We show that GCD has the best network classification performance, is highly noise-tolerant, and is computationally efficient. Using this methodology, we highlight a three-layer organization in the WTNs: core, broker, and periphery. Furthermore, we uncover the link between the dynamic changes in oil price and trade network topology.

Network models should shed light on the rules governing the formation of real networks. Using GCD, we identify models that fit five real-world network types. However, none of these standard network models fit WTNs. Hence, we introduce two new network models: one that mimics the Gravity Model of Trade, and the other that mimics brokerage / peripheral positioning of a country in WTN. Also, we show that economic wealth indicators of a country are predictive of its future brokerage position. Finally, we use exponential-family random graph modelling approach to build a generic framework that enables modelling based on any graphlet property.