Mathematical modeling of complex networks starts with a description of network data in terms of key structural features of the described network. This description constrained ensemble of random networks, whose constraints range in complexity from using the entire network structure (message passing approaches) to only using its degree distribution (configuration model) or density (Erdős-Rényi graphs). However, none of the resulting analytical descriptions are exact on complex networks and it is rarely clear when a more complicated model is justified by the data or by the quality of predictions. We will review new advances in network analyses and network descriptions to draw parallels between network modelling and network compression. In doing so, we outline a possible agenda for the future of mathematical network models.
Laurent Hébert-Dufresne obtained his PhD in physics in from Université Laval in Québec. He then branched out in different avenues of complex systems modeling; first in microbial and forest ecology as a James S. McDonnell Foundation Fellow at the Santa Fe Institute, and later as a researcher at the Institute for Disease Modeling. Now at the Vermont Complex Systems Center, he co-leads the modeling arm of the Joint Lab whose research focuses on the interaction and coevolution of structure and dynamics. Recent examples include social networks interacting with the spread of diseases and ideas, the interplay of plant-pollinator dynamics with commercial honeybee colonies and sustainable agriculture, and the modeling of learning mechanisms in multidisciplinary team work. More information can be found at https://joint-lab.github.io/.
Laurent Hébert-Dufresne obtained his PhD in physics in from Université Laval in Québec. He then branched out in different avenues of complex systems modeling; first in microbial and forest ecology as a James S. McDonnell Foundation Fellow at the Santa Fe Institute, and later as a researcher at the Institute for Disease Modeling. Now at the Vermont Complex Systems Center, he co-leads the modeling arm of the Joint Lab whose research focuses on the interaction and coevolution of structure and dynamics. Recent examples include social networks interacting with the spread of diseases and ideas, the interplay of plant-pollinator dynamics with commercial honeybee colonies and sustainable agriculture, and the modeling of learning mechanisms in multidisciplinary team work. More information can be found at https://joint-lab.github.io/.
