I have and am curretly participating in a variety of groups dedicated to researching many phenomena broadly falling under the label “higher-order network theory,” though I encourage the reader not to attempt too brazzen of categorizations on scientific research.

Research Projects

Multiplex Reconstruction and Inference

In collaboration with Siddharth Patwardhan, Minsuk Kim, and Filippo Radicchi.

Networks are becomingly increasingly popular as a modeling tool for complicated relational systems. Classical network science of the last century, including its explosion in the last couple decades, however, does not handle multi-dimensional interactions very well. One of the primary generalizations of networks into models of interactions with different types is the multiplex, a collection of networks with equivalent nodes but edges corresponding to different types of relations. These are known to more faithfully model realistic dynamics and structure of a variety of systems, however, observing them is not always done easily, without error or even at all. Often, only a single-layer aggregate form of the system’s network structure is available.

We are exploring ways in which to infer the original multiplex network topology from sort sort of compressed aggregate, including identifying bounds on when it is possible at all and what information is needed to do so.

Associated papers:

• D. Kaiser, S. Patwardhan, and F. Radicchi, Multiplex Reconstruction with Partial Information, Phys. Rev. E 107, 024309 (2023).
• [Under review] D. Kaiser, S. Patwardhan, M. Kim, and F. Radicchi, Reconstruction of multiplex networks via graph embeddings, (2023).

Hypergraph Clustering

In collaboration with Ilya Amburg, Jessalyn Bolkema, Philip Chodrow, Thomas Grubb, Jamie Haddock, Bill Kay, Jurgen Kritschgau, Fangfei Lan, Sepideh Maleki, and Oliver Alvarado Rodriguez.

Community detection in networks has a natural interpretation as a form of data compression; consequently, an information-theoretic lens can be applied to diagnosing optimal graph compressions via community detection.

Extending foundational work in dyadic network theory, we are exploring the use of entropy-based measures in clustering systems modeled by hypergraphs.

Associated papers:

• [Under review] J. Kritschgau, D. Kaiser, O. Alvarado Rodriguez, I. Amburg, J. Bolkema, T. Grubb, F. Lan, S. Maleki, P. Chodrow, and B. Kay, Community Detection in Hypergraphs via Mutual Information Maximization, (2023).

Research talks:

• Joint Mathematics Meetings 2023
  • “An Information-Theoretic Framework for Hypergraph Clustering” - presented by Ilya Amburg
  • “Information-Theoretic Hypergraph Clustering” - presented by Jessalyn Bolkema

Overlapping Community Structure and Contagion Dynamics

In collaboration with Varun Rao.

Contagion dynamics on networks are known to be affected by community structure; however, the role of overlapping communities on contagion dynamics is under-explored.

We are exploring consequences of overlapping community structure on the dynamics of complex contagions.