diff options
author | Paula PĂ©rez Bianchi <44149844+paulitapb@users.noreply.github.com> | 2023-03-21 05:48:16 -0300 |
---|---|---|
committer | GitHub <noreply@github.com> | 2023-03-21 14:18:16 +0530 |
commit | 0a114ae30bece92b80880d99fe156ce418796d5d (patch) | |
tree | da2e521e3afa3a84fcc9ee466ac3dabc7da0713f /networkx | |
parent | 02f23bc5a76544e3f0111aab75b73831cf59687a (diff) | |
download | networkx-0a114ae30bece92b80880d99fe156ce418796d5d.tar.gz |
Update docstring of paley graph (#6529)
* Add warning in community doc
* fix unwanted change
* Add latex formatting
* let pre-commit add double backslashes
* Update networkx/generators/expanders.py
Co-authored-by: Dan Schult <dschult@colgate.edu>
* Update networkx/generators/expanders.py
Co-authored-by: Dan Schult <dschult@colgate.edu>
* format docstring as raw to use normal latex
---------
Co-authored-by: Dan Schult <dschult@colgate.edu>
Diffstat (limited to 'networkx')
-rw-r--r-- | networkx/generators/expanders.py | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/networkx/generators/expanders.py b/networkx/generators/expanders.py index c48620dd..aac8c109 100644 --- a/networkx/generators/expanders.py +++ b/networkx/generators/expanders.py @@ -146,19 +146,19 @@ def chordal_cycle_graph(p, create_using=None): def paley_graph(p, create_using=None): - """Returns the Paley $\\frac{(p-1)}{2}$ -regular graph on $p$ nodes. + r"""Returns the Paley $\frac{(p-1)}{2}$ -regular graph on $p$ nodes. - The returned graph is a graph on $\\mathbb{Z}/p\\mathbb{Z}$ with edges between $x$ and $y$ - if and only if $x-y$ is a nonzero square in $\\mathbb{Z}/p\\mathbb{Z}$. + The returned graph is a graph on $\mathbb{Z}/p\mathbb{Z}$ with edges between $x$ and $y$ + if and only if $x-y$ is a nonzero square in $\mathbb{Z}/p\mathbb{Z}$. - If $p \\equiv 1 \\pmod 4$, $-1$ is a square in $\\mathbb{Z}/p\\mathbb{Z}$ and therefore $x-y$ is a square if and + If $p \equiv 1 \pmod 4$, $-1$ is a square in $\mathbb{Z}/p\mathbb{Z}$ and therefore $x-y$ is a square if and only if $y-x$ is also a square, i.e the edges in the Paley graph are symmetric. - If $p \\equiv 3 \\pmod 4$, $-1$ is not a square in $\\mathbb{Z}/p\\mathbb{Z}$ and therefore either $x-y$ or $y-x$ - is a square in $\\mathbb{Z}/p\\mathbb{Z}$ but not both. + If $p \equiv 3 \pmod 4$, $-1$ is not a square in $\mathbb{Z}/p\mathbb{Z}$ and therefore either $x-y$ or $y-x$ + is a square in $\mathbb{Z}/p\mathbb{Z}$ but not both. Note that a more general definition of Paley graphs extends this construction - to graphs over $q=p^n$ vertices, by using the finite field $F_q$ instead of $\\mathbb{Z}/p\\mathbb{Z}$. + to graphs over $q=p^n$ vertices, by using the finite field $F_q$ instead of $\mathbb{Z}/p\mathbb{Z}$. This construction requires to compute squares in general finite fields and is not what is implemented here (i.e `paley_graph(25)` does not return the true Paley graph associated with $5^2$). |