
arXiv: 1802.02146
Let $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\in V(H)$. Denote by $\varepsilon(H)$ the difference of the spectral radius of $H$ and the average degree of $H$. Also, denote \[ s(H)=\sum_{i\in V(H)}\left|d_i-\frac{rm}{n}\right|,~ v(H)=\frac{1}{n}\sum_{i\in V(H)}d_i^{\frac{r}{r-1}}-\left(\frac{rm}{n}\right)^{\frac{r}{r-1}}. \] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs.
14 pages
spectral radius, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Hypergraphs, \(r\)-uniform hypergraph, 15A42, 05C50
spectral radius, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Hypergraphs, \(r\)-uniform hypergraph, 15A42, 05C50
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 7 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
