Kun Dong (third-year Ph.D. student in the Center for Applied Mathematics at Cornell), Austin Benson (Assistant Professor of Computer Science), and David Bindel (Associate Professor of Computer Science) received a best research paper award for their work “The Structure and Interpretation of Graph Spectral Densities” at KDD ’19 (the SIGKDD Conference on Knowledge Discovery and Data Mining) held in Anchorage, Alaska. Bindel also delivered a plenary talk on the same topic—sponsored by the SIAM Activity Group on Linear Algebra or SIAG/LA—at the International Linear Algebra Society (ILAS) meeting in Rio De Janeiro.

Bindel describes the significance of the paper by noting that the research “takes computational and theoretical tools that are common in areas such as geometry and material science, and adapts those tools to improve our understanding of large, complex, real-world networks describing biological, social, and information systems. These tools show promise in helping us classify networks and in understanding the role played by different nodes in a network.” 

In a more detailed abstract, we learn that the research paper involves ongoing work in “the analysis of graphs via global summaries of the eigenvalue distributions and eigenvector behavior.” And that their “approach is drawn from the condensed matter physics literature, where the idea of local and global densities of states is often used to understand the electronic structure of systems.” The researchers “describe how these densities play a common role in such seemingly disparate topics as spectral geometry, condensed matter physics, and the study of centrality measures in graphs” and they “discuss how structural motifs manifest in the spectrum, give fast algorithms to estimate spectral densities.” Dong, Benson, and Bindel “conclude with a discussion of some of [their] current research directions in applying these tools to the analysis of large-scale graphs.”