MassExodus: modeling evolving networks in harsh environments

Evidence of Rentian Scaling of Functional Modules in Diverse Biological Networks

Biological networks have long been known to be modular, containing sets of nodes that are highly connected internally. Less emphasis, however, has been placed on understanding how intermodule connections are distributed within a network. Here, we borrow ideas from engineered circuit design and study Rentian scaling, which states that the number of external connections between nodes in different modules is related to the number of nodes inside the modules by a power-law relationship. We tested this property in a broad class of molecular networks, including protein interaction networks for six species and gene regulatory networks for 41 human and 25 mouse cell types. Using evolutionarily defined modules corresponding to known biological processes in the cell, we found that all networks displayed Rentian scaling with a broad range of exponents. We also found evidence for Rentian scaling in functional modules in the Caenorhabditis elegans neural network, but, interestingly, not in three different social networks, suggesting that this property does not inevitably emerge. To understand how such scaling may have arisen evolutionarily, we derived a new graph model that can generate Rentian networks given a target Rent exponent and a module decomposition as inputs. Overall, our work uncovers a new principle shared by engineered circuits and biological networks.

Learning the Structural Vocabulary of a Network

Networks have become instrumental in deciphering how information is processed and transferred within systems in almost every scientific field today. Nearly all network analyses, however, have relied on humans to devise structural features of networks believed to be most discriminative for an application. We present a framework for comparing and classifying networks without human-crafted features using deep learning. After training, autoencoders contain hidden units that encode a robust structural vocabulary for succinctly describing graphs. We use this feature vocabulary to tackle several network mining problems and find improved predictive performance versus many popular features used today. These problems include uncovering growth mechanisms driving the evolution of networks, predicting protein network fragility, and identifying environmental niches for metabolic networks. Deep learning offers a principled approach for mining complex networks and tackling graph-theoretic problems.

Self-Similarity in Social Network Dynamics

Analyzing and modeling social network dynamics are key to accurately predicting resource needs and system behavior in online social networks. The presence of statistical scaling properties, that is, self-similarity, is critical for determining how to model network dynamics. In this work, we study the role that self-similarity scaling plays in a social network edge creation (that is, links created between users) process, through analysis of two detailed, time-stamped traces, a 199 million edge trace over 2 years in the Renren social network, and 876K interactions in a 4-year trace of Facebook. Using wavelet-based analysis, we find that the edge creation process in both networks is consistent with self-similarity scaling, once we account for periodic user activity that makes edge creation process non-stationary. Using these findings, we build a complete model of social network dynamics that combines temporal and spatial components. Specifically, the temporal behavior of our model reflects self-similar scaling properties, and accounts for certain deterministic non-stationary features. The spatial side accounts for observed long-term graph properties, such as graph distance shrinkage and local declustering. We validate our model against network dynamics in Renren and Facebook datasets, and show that it succeeds in producing desired properties in both temporal patterns and graph structural features.