1 citations · 1 across the 4 of their papers we have counts for
6 papers
Comparing Eigenvector and Degree Dispersion with the Principal Ratio of a Graph
Gregory J. Clark
The principal ratio of a graph is the ratio of the greatest and least entry of its principal eigenvector. Since the principal ratio compares the extreme values of the principal eig…
On the Effect of Data Dimensionality on Eigenvector Centrality
Gregory J. Clark, Felipe Thomaz, Andrew Stephen
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets whic…
Applications of the Harary-Sachs Theorem for Hypergraphs
Gregory J. Clark, Joshua Cooper
The Harary-Sachs theorem for -uniform hypergraphs equates the codegree- coefficient of the adjacency characteristic polynomial of a uniform hypergraph with a weighted sum of…
A Harary-Sachs Theorem for Hypergraphs
Gregory J. Clark, Joshua Cooper
We generalize the Harary-Sachs theorem to -uniform hypergraphs: the codegree- coefficient of the characteristic polynomial of a uniform hypergraph can be expressed…
Leading Coefficients and the Multiplicity of Known Roots
Gregory J. Clark, Joshua N. Cooper
We show that a monic univariate polynomial over a field of characteristic zero, with distinct non-zero known roots, is determined by its proper leading coefficients by prov…
On the Adjacency Spectra of Hypertrees
Gregory J. Clark, Joshua Cooper
We extend the results of Zhang et al. to show that is an eigenvalue of a -uniform hypertree if and only if it is a root of a particular matching polynomial for…