48 citations · 112 across the 14 of their papers we have counts for
14 papers
Oriented hypergraphs and generalizing the Harary-Sachs theorem to integer matrices
Blake Dvarishkis, Josephine Reynes, Lucas J. Rusnak
Incidence-based generalizations of cycle covers, called contributors, extend the Harary-Sachs coefficient theorem for characteristic polynomials of the adjacency matrix of graphs.…
GraphC: Parameter-free Hierarchical Clustering of Signed Graph Networks v2
Muhieddine Shebaro, Lucas Rusnak, Martin Burtscher +1
Spectral clustering methodologies, when extended to accommodate signed graphs, have encountered notable limitations in effectively encapsulating inherent grouping relationships. Re…
Advances in Scaling Community Discovery Methods for Signed Graph Networks
Maria Tomasso, Lucas Rusnak, Jelena Tešić
Community detection is a common task in social network analysis (SNA) with applications in a variety of fields including medicine, criminology, and business. Despite the popularity…
The Determinant of -Matrices and Oriented Hypergraphs
Lucas J. Rusnak, Josephine Reynes, Russell Li +2
The determinants of -matrices are calculated by via the oriented hypergraphic Laplacian and summing over an incidence generalization of vertex cycle-covers. These cycle-…
Generalizing Kirchhoff laws for Signed Graphs
Lucas J. Rusnak, Josephine Reynes, Skyler J. Johnson +1
Kirchhoff-type Laws for signed graphs are characterized by generalizing transpedances through the incidence-oriented structure of bidirected graphs. The classical -arborescence…
Characterizing Attitudinal Network Graphs through Frustration Cloud
Lucas Rusnak, Jelena Tešić
Attitudinal Network Graphs are signed graphs where edges capture an expressed opinion; two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). A s…
Incidence Hypergraphs: Box Products & the Laplacian
Will Grilliette, Lucas J. Rusnak
The box product and its associated box exponential are characterized for the categories of quivers (directed graphs), multigraphs, set system hypergraphs, and incidence hypergraphs…
Oriented Hypergraphs: Balanceability
Lucas J. Rusnak, Selena Li, Brian Xu +2
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structu…
Incidence Hypergraphs: Injectivity, Uniformity, and Matrix-tree Theorems
Will Grilliette, Josephine Reynes, Lucas J. Rusnak
An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic subs…
Incidence hypergraphs: The categorical inconsistency of set-systems and a characterization of quiver exponentials
Will Grilliette, Lucas J. Rusnak
This paper considers the difficulty in the set-system approach to generalizing graph theory. These difficulties arise categorically as the category of set-system hypergraphs is sho…
Oriented Hypergraphic Matrix-tree Type Theorems and Bidirected Minors via Boolean Order Ideals
Ellen Robinson, Lucas J. Rusnak, Martin Schmidt +1
Restrictions of incidence-preserving path maps produce an oriented hypergraphic All Minors Matrix-tree Theorems for Laplacian and adjacency matrices. The images of these maps produ…
A Characterization of Oriented Hypergraphic Laplacian and Adjacency Matrix Coefficients
Gina Chen, Vivian Liu, Ellen Robinson +2
An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure.…
An Oriented Hypergraphic Approach to Algebraic Graph Theory
Nathan Reff, Lucas J. Rusnak
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of or . We define the adjacency, incidence and Laplacian matrices of an oriented h…
Oriented Hypergraphs I: Introduction and Balance
Lucas J. Rusnak
An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension o…