Higher-order geometry and topology of complex networks W911NF-17-S-0002
Abstract
We propose an interdisciplinary research program focused on development of novel theory, methods, and algorithms for higher order, non-dyadic interactions in complex networks and their functional implications. Complex networks underpin every area of current and future military and civilian infrastructure systems, and underpin integral parts of biological, physical, technological and socio-economic universe. Thus far, such networks have been mainly represented and analyzed as graphs with tools form graph theory used to analyze such systems. However, while graphs can capture pairwise interactions between nodes, fundamental interactions in networks often take place between multiple nodes. For example, in socio-economic networks, the joint coordinated activity of several agents (e.g. buyer, seller, broker); the formation and interactions of coalitions; and the existence of triadic closure are all prevalent. The objective of this interdisciplinary proposal is to investigate how such interactions can be taken into account via the use of simplicial complexes (SCs), extensions of graphs that go beyond pairwise interactions and systematically account for interactions between groups of nodes (triplets, quadruplets, etc.). By introducing a novel notion of diffusion on SCs, we will extend key diffusion based analysis techniques from graphs to the domain of SCs, thereby facilitating a more nuanced understanding of the studied systems. Specifically, we will study how to i) quantify the role edges in the information flow in a system; ii) predict group-based interactions; iii) use higher-order information for the detection of outliers and anomalies; and iv) detect mesoscale structures in higher-order data. We anticipate that this research will lead to a deepened understanding of the information-flow in networked systems, and could, e.g., lead to improved designs of communication structures in teams, or the detection of anomalies in communication patterns.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1910057
Entities
People
- Ali Jadbabaie
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army