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Gabrielle Demchak ’23

Major: Applied Mathematics
Project: The Harary Index as a Measure of Network Reliability
Advisor: Nathan Shank, professor of mathematics

Gabrielle Demchak ’23 wasn’t initially sure that the SOAR experience was for her, but after spending the summer delving into the mathematical principles of different graph classes, she found a rewarding experience in designing her own project with the support of an engaged team.

“The experience did not seem to be something I would enjoy,” Demchak says. “However, when I talked with [my advisor] Dr. Shank, he explained that the program is what you make of it, and I am so happy I went for it.”

The focus of Demchak’s research was a method of assessing graph types called the Harary index. This index functions as a way to measure reliability of different graph classes. Demchak and her team generated model parameters for different graph classes, then identified or created graphs that fit these.

“Originally, our group decided to do a graph-theory-based project,” Demchak says. “We were doing a literature search and found this new parameter, the Harary index. Through some discussion, we then came up with our research question, which revolved around the use of the Harary index as a measurement of reliability.”

Demchak found that conducting research allowed her to build a collaborative relationship with her advisor. “In class, it is more of a teacher-student relationship, but through this research, we worked more as colleagues trying to solve the same problem,” Demchak says. “Dr. Shank taught me fluidity in decision-making, because sometimes when we tried one way to approach the problem, we hit a dead end and then had to pivot.”

Demchak had a unique experience in the SOAR program. She worked in conjunction with the ̽������ Research Experience for Undergraduates (REU) program, which allowed her to collaborate with a variety of students and faculty, in addition to participating in panels with previous REU students to learn about their paths.

“I was able to learn so much from others’ experiences and thought processes,” Demchak shares. “This whole experience also opened my eyes to all the ways that mathematics impacts the world.”

Demchak speaks highly of the flexibility of skills she gained from SOAR. “Even if this is not your career choice,” she emphasizes, “this experience provides many soft skills and speaking opportunities, as well as time management, which are all transferable and useful skills.”

Demchak and her team presented at the Joint Math Meeting in 2022, as well as the eastern Pennsylvania and Delaware (EPaDel) section of the Mathematical Association of America conference.