Geometry of Complex Networks
Networks are ubiquitous in complex social, physical, biological, and engineered systems. Electrical energy is delivered by the power grid, the Internet enables almost instantaneous world-wide interactions, and our economies rest upon a complex network of interdependencies spanning the globe. Understanding the dynamics of these systems is essential for navigating, guiding, or designing them for desired behavior.
Much data contains higher-order interactions that take place among more than two entities: individuals communicate in small groups, not just pairs (for example, group chat messaging); people form small teams; and sensors record collections of interactions at a given time. Current models do not capture the rich, higher-order structure of these networks.
Austin Benson and Jon Kleinberg, Computer Science, are investigating how such interactions can be taken into account via the use of simplicial complexes—extensions of graphs that go beyond pairwise interactions and systematically account for interactions between groups of nodes (triplets, quadruplets, as examples).
Benson and Kleinberg, in collaboration with Ali Jadbabaie at MIT, are extending key diffusion-based analysis techniques from graphs to the domain of simplicial complexes, thereby facilitating a more nuanced understanding of the studied systems.
The research will lead to a deepened understanding of the information-flow in networked systems. It could also lead to improved designs of communication structures in teams, or the detection of anomalies in communication patterns.