Each year, millions of Americans move from one state to another, creating migration patterns that are far more complex than simple lists of where people are coming from or going to. Using traditional tools, the data confirms what we already know: California sees significant numbers of residents moving out. But when Manohar Murthi and Kamal Premaratne, faculty members at the University of Miami College of Engineering, analyzed the same Census data with a new method, a clearer picture emerged. Their approach showed groups of states with unusually strong two-way movement, including a cluster of Midwestern states that consistently exchange residents with one another, an insight that is not visible in standard summaries of the data.
The finding comes from a technique the researchers developed to study networks, which are often represented as graphs made up of points and the connections among them. Most tools focus on the points, known as vertices, and look for similarities among them. Although useful, this analysis can overlook how activity moves through the system, especially when a point plays several different roles. For example, a state may receive new residents from neighboring regions while seeing many of its own residents move elsewhere, creating overlapping patterns that are difficult to see when looking only at totals.
Murthi and Premaratne instead centered their analysis on the connections between points, known as edges. By examining which edges behave similarly, their method identifies meaningful subgraphs that highlight where activity originates, how it travels through the network and where it becomes concentrated. In the migration example, this approach made it possible to see regional movement patterns that are difficult to detect when focusing solely on individual states.
To support this analysis, the researchers designed a set of mathematical tools called flow Laplacians, which capture different types of directed movement within a network. These tools form the foundation of an edge spectral clustering framework that is both efficient and widely applicable. The method was also applied to other real-world scenarios, uncovering patterns such as distinctive traffic flow regions in a European roadway network and major pathways of carbon transfer within a Florida wetlands food web.
Murthi and Premaratne presented their work at the 16th IEEE International Conference on Knowledge Graphs, held Nov. 13 and 14 in Limassol, Cyprus. Their paper, "Clustering Edges Reveals How Vertices Exert Influence in Graph Data," received the conference's Best Paper Award, along with a monetary prize from IEEE, the leading professional organization for electrical and computer engineers.
