diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index da977ca338f..7ffeebbbc20 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -43,6 +43,10 @@ See the tidyverse guide on [how to create a great issue](https://code-review.tid
 
 *  We use [testthat](https://cran.r-project.org/package=testthat) for unit tests. 
    Please add test cases for the change you are proposing, or ask us for help.
+   
+### Naming conventions
+
+* Use `max` for maximal and `largest` for maximum.
 
 ### Test files
 
diff --git a/NAMESPACE b/NAMESPACE
index 976df8fc2a4..f9b1d4851d9 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -665,6 +665,7 @@ export(max_cliques)
 export(max_cohesion)
 export(max_degree)
 export(max_flow)
+export(max_ivs)
 export(maxcohesion)
 export(maximal.cliques)
 export(maximal.cliques.count)
diff --git a/R/cliques.R b/R/cliques.R
index 6388c8fbd91..6798fe11682 100644
--- a/R/cliques.R
+++ b/R/cliques.R
@@ -4,14 +4,14 @@
 #' @description
 #' `r lifecycle::badge("deprecated")`
 #'
-#' `maximal.independent.vertex.sets()` was renamed to `maximal_ivs()` to create a more
+#' `maximal.independent.vertex.sets()` was renamed to `max_ivs()` to create a more
 #' consistent API.
-#' @inheritParams maximal_ivs
+#' @inheritParams max_ivs
 #' @keywords internal
 #' @export
 maximal.independent.vertex.sets <- function(graph) { # nocov start
-  lifecycle::deprecate_soft("2.0.0", "maximal.independent.vertex.sets()", "maximal_ivs()")
-  maximal_ivs(graph = graph)
+  lifecycle::deprecate_soft("2.0.0", "maximal.independent.vertex.sets()", "max_ivs()")
+  max_ivs(graph = graph)
 } # nocov end
 
 #' Functions to find cliques, i.e. complete subgraphs in a graph
@@ -382,7 +382,7 @@ weighted_clique_num <- weighted_clique_number_impl
 #' sets in the graph. An independent vertex set is largest if there is no
 #' independent vertex set with more vertices.
 #'
-#' `maximal_ivs()` finds the maximal independent vertex
+#' `max_ivs()` finds the maximal independent vertex
 #' sets in the graph. An independent vertex set is maximal if it cannot be
 #' extended to a larger independent vertex set. The largest independent vertex
 #' sets are maximal, but the opposite is not always true.
@@ -401,7 +401,7 @@ weighted_clique_num <- weighted_clique_number_impl
 #'   vertex sets to find. `NULL` means no limit.
 #' @return `ivs()`,
 #'   `largest_ivs()` and
-#'   `maximal_ivs()` return a list containing numeric
+#'   `max_ivs()` return a list containing numeric
 #'   vertex ids, each list element is an independent vertex set.
 #'
 #'   `ivs_size()` returns an integer constant.
@@ -428,7 +428,7 @@ weighted_clique_num <- weighted_clique_number_impl
 #' # Empty graph
 #' induced_subgraph(g, largest_ivs(g)[[1]])
 #'
-#' length(maximal_ivs(g))
+#' length(max_ivs(g))
 ivs <- function(graph, min = NULL, max = NULL) {
   ensure_igraph(graph)
 
@@ -472,7 +472,7 @@ largest_ivs <- function(graph) {
 
 #' @rdname ivs
 #' @export
-maximal_ivs <- function(graph) {
+max_ivs <- function(graph) {
   ensure_igraph(graph)
 
   on.exit(.Call(R_igraph_finalizer))
@@ -486,6 +486,21 @@ maximal_ivs <- function(graph) {
   res
 }
 
+#' Maximal independent vertex sets in the graph
+#'
+#' @description
+#' `r lifecycle::badge("deprecated")`
+#'
+#' `maximal_ivs()` was renamed to `max_ivs()` to create a more
+#' consistent API.
+#' @export
+#' @inheritParams max_ivs
+#' @keywords internal
+maximal_ivs <- function(graph) {
+  lifecycle::deprecate_soft("2.0.4", "maximal_ivs()", "max_ivs()")
+  max_ivs(graph)
+}
+
 #' @rdname ivs
 #' @export
 ivs_size <- function(graph) {
diff --git a/inst/lifecycle/deprecated.csv b/inst/lifecycle/deprecated.csv
index bb265a7c93d..51307fc8bff 100644
--- a/inst/lifecycle/deprecated.csv
+++ b/inst/lifecycle/deprecated.csv
@@ -186,7 +186,7 @@ list.vertex.attributes,<a href='https://r.igraph.org/reference/vertex_attr_names
 maxcohesion,<a href='https://r.igraph.org/reference/cohesive_blocks.html'>igraph::max_cohesion</a>
 maximal.cliques,<a href='https://r.igraph.org/reference/cliques.html'>igraph::max_cliques</a>
 maximal.cliques.count,<a href='https://r.igraph.org/reference/cliques.html'>igraph::count_max_cliques</a>
-maximal.independent.vertex.sets,<a href='https://r.igraph.org/reference/ivs.html'>igraph::maximal_ivs</a>
+maximal.independent.vertex.sets,<a href='https://r.igraph.org/reference/ivs.html'>igraph::max_ivs</a>
 minimal.st.separators,<a href='https://r.igraph.org/reference/min_st_separators.html'>igraph::min_st_separators</a>
 maximum.bipartite.matching,<a href='https://r.igraph.org/reference/matching.html'>igraph::max_bipartite_match</a>
 maximum.cardinality.search,<a href='https://r.igraph.org/reference/max_cardinality.html'>igraph::max_cardinality</a>
diff --git a/man/ivs.Rd b/man/ivs.Rd
index ef9c3c443c5..caf2f80ad10 100644
--- a/man/ivs.Rd
+++ b/man/ivs.Rd
@@ -3,7 +3,7 @@
 \name{ivs}
 \alias{ivs}
 \alias{largest_ivs}
-\alias{maximal_ivs}
+\alias{max_ivs}
 \alias{ivs_size}
 \title{Independent vertex sets}
 \usage{
@@ -11,7 +11,7 @@ ivs(graph, min = NULL, max = NULL)
 
 largest_ivs(graph)
 
-maximal_ivs(graph)
+max_ivs(graph)
 
 ivs_size(graph)
 }
@@ -28,7 +28,7 @@ vertex sets to find. \code{NULL} means no limit.}
 \value{
 \code{ivs()},
 \code{largest_ivs()} and
-\code{maximal_ivs()} return a list containing numeric
+\code{max_ivs()} return a list containing numeric
 vertex ids, each list element is an independent vertex set.
 
 \code{ivs_size()} returns an integer constant.
@@ -47,7 +47,7 @@ arguments.
 sets in the graph. An independent vertex set is largest if there is no
 independent vertex set with more vertices.
 
-\code{maximal_ivs()} finds the maximal independent vertex
+\code{max_ivs()} finds the maximal independent vertex
 sets in the graph. An independent vertex set is maximal if it cannot be
 extended to a larger independent vertex set. The largest independent vertex
 sets are maximal, but the opposite is not always true.
@@ -71,7 +71,7 @@ largest_ivs(g)
 # Empty graph
 induced_subgraph(g, largest_ivs(g)[[1]])
 
-length(maximal_ivs(g))
+length(max_ivs(g))
 }
 \references{
 S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new
diff --git a/man/maximal.independent.vertex.sets.Rd b/man/maximal.independent.vertex.sets.Rd
index 9e53faec2d5..c1cfd4ccecc 100644
--- a/man/maximal.independent.vertex.sets.Rd
+++ b/man/maximal.independent.vertex.sets.Rd
@@ -13,7 +13,7 @@ loop edges and multiple edges are ignored.}
 \description{
 \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
 
-\code{maximal.independent.vertex.sets()} was renamed to \code{maximal_ivs()} to create a more
+\code{maximal.independent.vertex.sets()} was renamed to \code{max_ivs()} to create a more
 consistent API.
 }
 \keyword{internal}
diff --git a/man/maximal_ivs.Rd b/man/maximal_ivs.Rd
new file mode 100644
index 00000000000..d469785305b
--- /dev/null
+++ b/man/maximal_ivs.Rd
@@ -0,0 +1,19 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/cliques.R
+\name{maximal_ivs}
+\alias{maximal_ivs}
+\title{Maximal independent vertex sets in the graph}
+\usage{
+maximal_ivs(graph)
+}
+\arguments{
+\item{graph}{The input graph, directed graphs are considered as undirected,
+loop edges and multiple edges are ignored.}
+}
+\description{
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
+
+\code{maximal_ivs()} was renamed to \code{max_ivs()} to create a more
+consistent API.
+}
+\keyword{internal}