From e631ffb0dd252bc62a6789567f42a4a11fe9098a Mon Sep 17 00:00:00 2001
From: schochastics <david@schochastics.net>
Date: Fri, 2 Dec 2022 16:47:28 +0100
Subject: [PATCH] addressed review
 https://github.com/openjournals/joss-reviews/issues/4987#issuecomment-1335336761

---
 paper.bib | 35 +++++++++++++++++++++++++++++++++++
 paper.md  | 19 ++++++++++++-------
 2 files changed, 47 insertions(+), 7 deletions(-)

diff --git a/paper.bib b/paper.bib
index 74d7477..d2a397f 100644
--- a/paper.bib
+++ b/paper.bib
@@ -215,3 +215,38 @@ @misc{fmtk-ergmdsnair-22
   publisher = {{arXiv}},
   doi = {10.48550/arXiv.2205.13411}
 }
+
+@article{an-dcopsnpc-20,
+  title = {Detecting Coalitions by Optimally Partitioning Signed Networks of Political Collaboration},
+  author = {Aref, Samin and Neal, Zachary},
+  year = {2020},
+  journal = {Scientific Reports},
+  volume = {10},
+  number = {1},
+  pages = {1506},
+  publisher = {{Nature Publishing Group}},
+  issn = {2045-2322},
+  doi = {10.1038/s41598-020-58471-z}
+}
+
+@manual{s-omsmilp-22,
+  title = {ompr: Model and Solve Mixed Integer Linear Programs},
+  author = {Dirk Schumacher},
+  year = {2022},
+  note = {R package version 1.0.3},
+  url = {https://CRAN.R-project.org/package=ompr},
+}
+
+@article{n-brpenb-22,
+    doi = {10.1371/journal.pone.0269137},
+    author = {Neal, Zachary P.},
+    journal = {PLOS ONE},
+    publisher = {Public Library of Science},
+    title = {backbone: An {{R}} package to extract network backbones},
+    year = {2022},
+    month = {05},
+    volume = {17},
+    url = {https://doi.org/10.1371/journal.pone.0269137},
+    pages = {1-24},
+    number = {5}
+}
diff --git a/paper.md b/paper.md
index 397a624..6e84e84 100644
--- a/paper.md
+++ b/paper.md
@@ -42,8 +42,9 @@ social media [@klb-szmsnne-09]. General purpose packages for network analysis
 such as `igraph` [@cn-ispcnr-06] and `sna` [@b-snas-08] implement all commonly
 used network analytic methods but do not offer any functionality for signed
 networks. `signnet` closes this gap and makes many tools for signed
-network available in R. The package has already found its place in empirical research
-[@csr-avacpbsn-22;@fmtk-ergmdsnair-22].
+networks available in R. The package has already found its place in empirical research
+[@csr-avacpbsn-22;@fmtk-ergmdsnair-22] and the R package `backbone` [@n-brpenb-22] uses the data 
+structure suggested by `signnet` for signed backbones of networks.  
 
 # Implementation details
 The package is modeled with `igraph` compatibility in mind and follows its
@@ -60,6 +61,7 @@ This section highlights some of the main methods implemented in the package.
 For more details for each subsection see the respective package vignette. 
 
 ```R
+install.packages("signnet"")
 library(signnet)
 data("tribes") # dataset included in signnet
 ```
@@ -93,8 +95,11 @@ frustration_exact(tribes)
 ```
 
 The return value `partition` gives the optimal partition into the two node sets for 
-which the optimal frustration is achieved. Note that the problem is NP hard and 
-frustration can thus only be calculated for rather small signed networks.
+which the optimal frustration is achieved. The implemented algorithm can deal with fairly large 
+networks, even though the problem is NP hard [@an-dcopsnpc-20].
+
+To use `frustation_exact()`, the package `ompr` and its auxiliary packages need to be installed
+separately [@s-omsmilp-22].
 
 ## Blockmodeling
 In signed blockmodeling, the goal is to determine $k$ blocks of nodes such that
@@ -163,11 +168,11 @@ pn_index(g)
 
 ## Signed two-mode networks
 A common analytic tool for two-mode networks is to project the network onto on
-relevant mode. This is easily done using the adjacency matrix $𝐴$. $𝐴𝐴^𝑇$
-yields the row projection and $𝐴^𝑇𝐴$ the column projection. The resulting
+relevant mode. This is easily done using the adjacency matrix $A$. $AA^T$
+yields the row projection and $A^TA$ the column projection. The resulting
 networks will thus be weighted. Several methods exist to turn a weighted
 projection into an unweighted network where only the most significant edges are
-included [@dns-brpebbp-21]. Projecting signed networks is not as
+included [@n-brpenb-22]. Projecting signed networks is not as
 straightforward, because "nullification" of edges can occur. @s-pstn-21
 introduces two methods to deal with this issue which are implemented in
 `signnet`. The trick is to convert the signed network into an a special