Fifth-year physics graduate student Hyunju Kim of Daegu, Korea, produced the key elements for a mathematical physics paper that was selected as a “Fast Track Communication” of the Journal of Physics A: Mathematical and General.
According to the journal, Fast Track Communications are “outstanding short papers reporting new and timely developments in mathematical and theoretical physics.” The paper tackles a fundamental problem in graph theory, namely constructing all labeled graphs whose nodes have pre-specified degrees (nr of neighbors), a result with key implications also on graph sampling.
Kim’s adviser, Prof. Zoltán Toroczkai of the University of Notre Dame’s Physics Department and director of Notre Dame’s Interdisciplinary Center for Network Science and Applications (iCeNSA) elaborates: “Hyunju came up with crucial ideas and proofs needed to solve one of the fundamental graph theoretical problems in network research. Her work has applications ranging from the study of the spread of diseases (epidemics), social networks, communication networks (Internet), to chemistry, particularly, counting structural isomers of alkanes.”
iCeNSA is an interdisciplinary research center organized around network science problems in social, biological, biochemical, physical, environmental, financial, organizational, technical and defense systems. Faculty and students at iCeNSA delve into the exploding research area of networks—how they emerge, what they look like, how they evolve, and how they impact our understanding of complex systems. Says Toroczkai: “We have found that a combination of statistical physics, graph theory and computational methods allows us to capture the topology of these diverse systems within a single framework.”
Kim will continue her work at iCeNSA throughout her tenure as a graduate student, performing research related to fundamental mathematical methods and its applications in network science—in particular, to the formation of functional modules in neuronal networks.