Research

Research Interests

I find it fascinating that we can use randomness to construct subtle objects, such as Ramsey graphs or optimal error-correcting codes. Even more interesting, however, is the fact that we can find deterministic objects which possess random-like properties, which can be formalized via a theory of quasirandomness. 

My favorite problems tend to arise from applications, often in data science or computer science. I am currently focused on the theoretical properties of small-world networks which are ubiquitous in data science. 

Papers and Preprints

• N. Sieger. Dense Subgraphs in Locally Quasirandom Graphs. In preparation.

  • We show that a graph where every vertex neighborhood is quasirandom must be close to a disjoint union of dense quasirandom graphs. 

• F. Chung, N. Sieger. Quasirandomness for Clustering Graphs. Submitted to Journal of Graph Theory.

  • Together with our results in Eigenvalues of Clustering Graphs, we show that every sufficiently large clustering graph can be decomposed into subgraphs where almost all vertices have a quasirandom neighborhood

• F. Chung, N. Sieger. Eigenvalues of Clustering Graphs. Linear Algebra and Its Applications, In Press, (2026).

  • Proved a stronger version of the regularity lemma for clustering graphs due to Chung

  • Introduced matrices which generalize the clustering coefficient and gave connections to cohomology and graph Laplacians.

• H. Pipp, N. Sieger. Algorithmic Apsects of the Clustering Regularity Lemma  Proceedings of the 21st Workshop on Algorithms and Models for the Web Graph (WAW 2026), 1-16, (2026).

• C. Buchanan, M. Carr, A. Clifton, S. Hartke, V. Irsic Chenoweth, N. Sieger, and R. Whitman. Trail Trap: A Variant of Partizan Edge Geography. Discrete Applied Mathematics, 379, 79–95. (2026).

• F. Chung, M. Rawson, Z. Shen, N. Sieger, and M. Xu,  Ricci Curvatures in Random Clustering Graphs. Journal of Combinatorics 16, 421–463, (2025).

• K. Celano, N. Sieger, and S. Spiro. Eulerian Polynomials for Digraphs. Combinatorial Theory, 5(1),  (2025). 

• F. Chung, and N. Sieger. Quasi-Random Influences of Boolean Functions. The Electronic Journal of Combinatorics, Volume 31, Issue 2, 2-52, (2024).

  • Proved a quasirandom equivalence theorem 

• M. Levet, P. Rombach, and N. Sieger. Canonizing Graphs of Bounded Rank-Width in Parallel via Weisfeiler-Leman. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 32:1-32:18, (2024). 

•  F. Chung and N. Sieger, Subgraph Counts for Random Clustering Graphs. Proceedings of the 19th Workshop on Algorithms and Models for the Web Graph (WAW 2024), 1-16, (2024).

• F. Chung and N. Sieger, A Random Graph Model for Clustering Graphs. Proceedings of the 18th Workshop on Algorithms and Models for the Web Graph (WAW 2023), 112-126, (2023).

• M. Fernandez, N. Sieger, and M. Tait. Maximal Planar Subgraphs of Fixed Girth in Random Graphs. The Electronic Journal of Combinatorics, 2-45,(2018).

Pictures

The main proof diagram (left) for my results in Quasi-random Influences for Boolean Functions and relationship between the extant classes of quasirandom Boolean functions (right) also in the same paper. 

Two related classes of clustering quasirandom graphs from Eigenvalues for Clustering Graphs and Quasirandomness for Clustering Graphs. In Dense Subgraphs in Locally Quasirandom Graphs, I show that locally quasirandom graphs must resemble these graphs with a partition into dense components. 

The various vertex sets which need to be controlled to analyze curvature of a single edge uv in a random clustering graph. From Ricci Curvatures in Random Clustering Graphs.