Complex systems are often characterized by a large collection of components interacting in nontrivial. Conceptual, mathematical, and computational tools are required for modeling and analyzing the interactions we observe at a macroscopic scale. A principled approach to understand these complex systems (and the processes that give rise to them) is to formulate generative models and infer their parameters from given data that is typically stored in the form of networks (or graphs). The increasing availability of network data from a wide variety of sources, such as the Internet, online social networks, collaboration networks, biological networks, etc., has fueled the rapid development of network science.
A variety of generative models have been designed to synthesize networks having specific properties (such as power law degree distributions, small-worldness etc.), leaving the modeler with the nontrivial task of choosing an appropriate one. A typical scenario where the modeler has limited knowledge about the specific model to use necessitates a robust framework for inferring a plausible network generative model from a set of network observations (typically only 1 observation). To alleviate the burden of choosing an appropriate model, machine learning and evolutionary algorithms can be used to automatically infer appropriate network generation mechanisms from the observed network structure.
Through a series of (not new) observations based on first principles, we extrapolate an action-based framework that creates a compact probabilistic model for synthesizing real-world networks using a single network observation. Our action-based perspective assumes that the generative process is composed of two main components: (1) a set of actions that expresses link formation potential using different strategies capturing the collective behavior of nodes, and (2) an algorithmic environment that provides opportunities for nodes to create links. Optimization and machine learning methods are used to learn an appropriate low-dimensional action-based representation for the network in the form of a row stochastic matrix, which can subsequently be used for simulating the system at various scales. We also show that in addition to being practically relevant, the proposed model is relatively exchangeable up to relabeling of the node types.
Further, we show that such a general model can find utility in various contexts by capturing different structural properties observed in networks across domains. For example, we use the action-based framework as a centralized approach for designing resilient supply chain networks and proposed a new variant to investigate the relationship between the patterns in structural brain connectivity and the cognitive ability of a human subject.