Tatyana Benko

Tatyana Benko, Rebecca Jones, Lucas Tate

Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between objects in a graph is often required. Given a larger graph and a smaller graph, one may wish to identify instances of the smaller query graph in the larger target graph. This task is called subgraph identification or matching. Subgraph matching is helpful in areas such as bioinformatics, binary analysis, pattern recognition, and computer vision. In these applications, datasets frequently contain noise and errors, thus exact subgraph matching algorithms do not apply. In this paper we introduce a new customizable algorithm for inexact subgraph matching. Our algorithm utilizes node and edge attributes which are often present in real-world datasets to narrow down the search space. The algorithm is flexible in the type of subgraph matching it can perform and the types of datasets it can process by its use of a modifiable graph edit distance cost function for pairing nodes. We show its effectiveness on family trees graphs and control-flow graphs.

Tatyana Benko, Martin Buck, Ilya Amburg et al.

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks.