A Generalized Framework for Representing Complex Networks

Complex systems are often characterized by a large collection of components interacting in nontrivial ways. Self-organization among these individual components often leads to emergence of a macroscopic structure that is neither completely regular nor completely random. In order to understand what we observe at a macroscopic scale, conceptual, mathematical, and computational tools are required for modeling and analyzing these interactions. 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.), but the structural richness of real-world network data calls for researchers to posit new models that are capable of keeping pace with the empirical observations about the topological properties of real networks. The mechanistic approach to modeling networks aims to identify putative mechanisms that can explain the dependence, diversity, and heterogeneity in the interactions responsible for creating the topology of an observed network. A successful mechanistic model can highlight the principles by which a network is organized and potentially uncover the mechanisms by which it grows and develops. While it is difficult to intuit appropriate mechanisms for network formation, machine learning and evolutionary algorithms can be used to automatically infer appropriate network generation mechanisms from the observed network structure.

Building on these philosophical foundations and 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. 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 an observed 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.

Such a model can facilitate handling many of the challenges of understanding real data, including accounting for noise and missing values, and connecting theory with data by providing interpretable results. To demonstrate the practicality of the action-based model, we decided to utilize the model within domain-specific contexts. We used the model as a centralized approach for designing resilient supply chain networks while incorporating appropriate constraints, a rare feature of most network models. Similarly, a new variant of the action-based model was used for understanding the relationship between the structural organization of human brains and the cognitive ability of subjects. Finally, our analysis of the ability of state-of-the-art network models to replicate the expected topological variations in network populations highlighted the need for rethinking the way we evaluate the goodness-of-fit of new and existing network models, thus exposing significant gaps in the literature.