Résumé : Many complex systems can successfully be described as networks. This abstracts away most particularities of individual units in the system and allows to highlight and study the effects of the complex structure of their connections. Notable examples are human interaction networks and the spread of contagions and information in these, biological networks, including biotic interactions in ecosystems and neural connections in the brain, infrastructural networks, and world trade. The structure and dynamics of most empirically measured networks are complex and intrinsically correlated, making it particularly challenging to study them using traditional generative models.

As an alternative to the bottom-up approach of generative models, randomized reference models (RRMs) constitute a top-down approach to studying complex networks. RRMs deal with the controlled destruction of given temporal or topological structures in a complex network in order to create a distribution of reference networks retaining certain features of the original network. They are typically implemented as procedures that shuffle the edges of the network while retaining the features in question. This makes RRMs very generally applicable, and in particular in cases where we are not able to specify a realistic generative model. However, the effects of most shuffling procedures on network features remain poorly understood, complicating the interpretation of results, and the lack of a common framework has made it difficult to compare different RRMs.

I will describe a unified framework for the important class of RRMs generated by uniform shuffling procedures, which we by analogy to statistical physics will name microcanonical RRMs (MRRMs). Our framework lets us build a taxonomy of MRRMs that orders them and deduces their effects on important network features. It additionally tells us how we may generate new MRRMs by combining existing ones. I will discuss how MRRMs may be used as null models to identify statistically significant features in empirical networks. I will show how our framework can be used when we do not know how to choose the correct null model, and will apply this to characterize computational motifs in the Drosophila larval brain. I will finally show how series of different MRRMs may be used to pick apart the effects of different features of a network on dynamical processes unfolding on it.

Reference : arXiv:1806.04032