Santa Fe Institute

Workshop: An overdue overhaul for network theory

Dec. 17, 2015 12:34 p.m.

Networks are everywhere – from social interactions to species feeding relationships to the algorithms that pull information from large datasets. Because of its broad utility in quantifying interacting systems, network theory now finds application in many disciplines. 

But network theory, like any emerging field, needs to keep up with the times.

A network is traditionally regarded as a static array of nodes connected by links, but an overhaul of that view is long overdue, says SFI Professor Cristopher Moore.

"Many of the models we've had in the past are too simple," says Moore, who dwells at the intersection of physics, mathematics, and computer science. "They don't capture the rich structure of real networks like power grids or food webs."

Networks should be approached not as static objects, but as dynamic systems that change in time, he says. Similarly, nodes and edges aren't flat and anonymous – they often have rich metadata, like location for nodes, or duration for edges – that should be incorporated into new models.

Moving beyond the antiquated view of networks is one goal of a mid-December SFI workshop, Inference on Networks: Algorithms, Phase Transitions, New Models, and New Data. Moore co-organized the meeting with computer scientist Aaron Clauset (University of Colorado Boulder) and physicist Mark Newman (University of Michigan), both SFI external professors.

The workshop’s other goal, Moore says, was to assemble researchers from disparate fields to forge novel insights. The last decade, he says, brought an “exciting flow of ideas” among physicists, mathematicians, and computer scientists who create algorithms appropriate for rich datasets and study the behaviors that emerge. But there is more to learn.

The interdisciplinary nature of the gathering is the key. “Physicists can make good guesses about algorithms and how well they perform,” he says. “Computer scientists can in some cases prove the physicists' conjectures that the algorithms we've found really are the best ones. Meanwhile, domain experts including ecologists and biologists can tell us when our models are relevant to their data. They connect the theory to practice.”

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