Selected Research Projects

Influential node and higher-order interactions detection on networks.

Identifying influential nodes in a complex network is an important graph mining problem with many diverse applications such as information propagation, market advertising, and rumor controlling. Influential nodes in a network play critical roles and largely affect network structure and functions more than the rest of the network. They are able to diffuse or spread information throughout a complex network more rapidly. In this project, we detect the important nodes and higher-order interactions in networks that have key roles in information diffusion.

Modeling diffusion on Hypergraphs.

Diffusion on networks is an important concept in network science that models how a stuff, such as information and heat, diffuses between vertices based on network topology, the pattern of who is connected to whom. In this project, we develop new hypergraph Laplacians to model diffusion more comprehensively.

Hypergraph classification.

Modern science and technology have witnessed in the past decade a proliferation of complex data that can be naturally modeled and interpreted as networks. For example, one can represent proteins as hypergraphs where nodes represent secondary structure elements and hyperedges indicate neighborhoods in the amino-acid sequence or in 3D space. In this project, we use TDA to classify biological and chemical networks such as whether or not chemical compounds have a mutagenic effect on a specific bacteria, or for activity against non-small cell lung cancer and ovarian cancer cell lines.