diff --git a/NAMESPACE b/NAMESPACE
index 0a5d6b24c38..3ad0778d3fe 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -140,6 +140,7 @@ export(as_adj)
 export(as_adj_edge_list)
 export(as_adj_list)
 export(as_adjacency_matrix)
+export(as_biadjacency_matrix)
 export(as_bipartite)
 export(as_data_frame)
 export(as_edgelist)
@@ -442,6 +443,7 @@ export(graph_attr_names)
 export(graph_from_adj_list)
 export(graph_from_adjacency_matrix)
 export(graph_from_atlas)
+export(graph_from_biadjacency_matrix)
 export(graph_from_data_frame)
 export(graph_from_edgelist)
 export(graph_from_graphdb)
diff --git a/R/adjacency.R b/R/adjacency.R
index c1d648a65c2..13053bb9a81 100644
--- a/R/adjacency.R
+++ b/R/adjacency.R
@@ -374,7 +374,7 @@ graph_from_adjacency_matrix <- function(adjmatrix,
 
   if (!is.matrix(adjmatrix) && !inherits(adjmatrix, "Matrix")) {
     lifecycle::deprecate_soft(
-      "1.5.2",
+      "1.6.0",
       "graph_from_adjacency_matrix(adjmatrix = 'must be a matrix')"
     )
     adjmatrix <- as.matrix(1)
@@ -383,7 +383,7 @@ graph_from_adjacency_matrix <- function(adjmatrix,
   if (mode == "undirected") {
     if (!is_symmetric(adjmatrix)) {
       lifecycle::deprecate_soft(
-        "1.5.2",
+        "1.6.0",
         "graph_from_adjacency_matrix(adjmatrix = 'must be symmetric with mode = \"undirected\"')",
         details = 'Use mode = "max" to achieve the original behavior.'
       )
diff --git a/R/bipartite.R b/R/bipartite.R
index 534cfc72478..46250da34c4 100644
--- a/R/bipartite.R
+++ b/R/bipartite.R
@@ -83,7 +83,7 @@
 #' colnames(M) <- c("Party", "Skiing", "Badminton")
 #' M[] <- sample(0:1, length(M), replace = TRUE)
 #' M
-#' g2 <- graph_from_incidence_matrix(M)
+#' g2 <- graph_from_biadjacency_matrix(M)
 #' g2$name <- "Event network"
 #' proj2 <- bipartite_projection(g2)
 #' print(proj2[[1]], g = TRUE, e = TRUE)
diff --git a/R/conversion.R b/R/conversion.R
index cbe7ce9b1af..ca0b1c3bc94 100644
--- a/R/conversion.R
+++ b/R/conversion.R
@@ -801,10 +801,10 @@ get.incidence.sparse <- function(graph, types, names, attr) {
 
 
 
-#' Incidence matrix of a bipartite graph
+#' Bipartite adjacency matrix of a bipartite graph
 #'
-#' This function can return a sparse or dense incidence matrix of a bipartite
-#' network. The incidence matrix is an \eqn{n} times \eqn{m} matrix, \eqn{n}
+#' This function can return a sparse or dense bipartite adjacency matrix of a bipartite
+#' network. The bipartite adjacency matrix is an \eqn{n} times \eqn{m} matrix, \eqn{n}
 #' and \eqn{m} are the number of vertices of the two kinds.
 #'
 #' Bipartite graphs have a `type` vertex attribute in igraph, this is
@@ -818,9 +818,9 @@ get.incidence.sparse <- function(graph, types, names, attr) {
 #'   `type` vertex attribute. You must supply this argument if the graph has
 #'   no `type` vertex attribute.
 #' @param attr Either `NULL` or a character string giving an edge
-#'   attribute name. If `NULL`, then a traditional incidence matrix is
+#'   attribute name. If `NULL`, then a traditional bipartite adjacency matrix is
 #'   returned. If not `NULL` then the values of the given edge attribute are
-#'   included in the incidence matrix. If the graph has multiple edges, the edge
+#'   included in the bipartite adjacency matrix. If the graph has multiple edges, the edge
 #'   attribute of an arbitrarily chosen edge (for the multiple edges) is
 #'   included.
 #' @param names Logical scalar, if `TRUE` and the vertices in the graph
@@ -831,16 +831,20 @@ get.incidence.sparse <- function(graph, types, names, attr) {
 #'   created, you will need the `Matrix` package for this.
 #' @return A sparse or dense matrix.
 #' @author Gabor Csardi \email{csardi.gabor@@gmail.com}
-#' @seealso [graph_from_incidence_matrix()] for the opposite operation.
+#' @seealso [graph_from_biadjacency_matrix()] for the opposite operation.
 #' @family conversion
 #' @export
 #' @keywords graphs
+#' @details
+#' Some authors refer to the bipartite adjacency matrix as the
+#' "bipartite incidence matrix". igraph 1.6.0 and later does not use
+#' this naming to avoid confusion with the edge-vertex incidence matrix.
 #' @examples
 #'
 #' g <- make_bipartite_graph(c(0, 1, 0, 1, 0, 0), c(1, 2, 2, 3, 3, 4))
-#' as_incidence_matrix(g)
+#' as_biadjacency_matrix(g)
 #'
-as_incidence_matrix <- function(graph, types = NULL, attr = NULL,
+as_biadjacency_matrix <- function(graph, types = NULL, attr = NULL,
                                 names = TRUE, sparse = FALSE) {
   # Argument checks
   ensure_igraph(graph)
@@ -855,11 +859,30 @@ as_incidence_matrix <- function(graph, types = NULL, attr = NULL,
     get.incidence.dense(graph, types = types, names = names, attr = attr)
   }
 }
-
+#' As incidence matrix
+#'
+#' @description
+#' `r lifecycle::badge("deprecated")`
+#'
+#' `as_incidence_matrix()` was renamed to `as_biadjacency_matrix()` to create a more
+#' consistent API.
+#' @inheritParams as_biadjacency_matrix
+#' @keywords internal
+#' @details
+#' Some authors refer to the bipartite adjacency matrix as the
+#' "bipartite incidence matrix". igraph 1.6.0 and later does not use
+#' this naming to avoid confusion with the edge-vertex incidence matrix.
+#' @export
+as_incidence_matrix <- function(...) { # nocov start
+   lifecycle::deprecate_soft("1.6.0", "as_incidence_matrix()", "as_biadjacency_matrix()")
+   as_biadjacency_matrix(...)
+} # nocov end
 #' @rdname graph_from_data_frame
 #' @param x An igraph object.
 #' @param what Character constant, whether to return info about vertices,
 #'   edges, or both. The default is \sQuote{edges}.
+#' @family conversion
+#' @family biadjacency
 #' @export
 as_data_frame <- function(x, what = c("edges", "vertices", "both")) {
   ensure_igraph(x)
diff --git a/R/incidence.R b/R/incidence.R
index 639c0608f3e..fcffb34e49c 100644
--- a/R/incidence.R
+++ b/R/incidence.R
@@ -137,36 +137,36 @@ graph.incidence.dense <- function(incidence, directed, mode, multiple,
   res
 }
 
-#' Create graphs from an incidence matrix
+#' Create graphs from a bipartite adjacency matrix
 #'
-#' `graph_from_incidence_matrix()` creates a bipartite igraph graph from an incidence
+#' `graph_from_biadjacency_matrix()` creates a bipartite igraph graph from an incidence
 #' matrix.
 #'
 #' Bipartite graphs have a \sQuote{`type`} vertex attribute in igraph,
 #' this is boolean and `FALSE` for the vertices of the first kind and
 #' `TRUE` for vertices of the second kind.
 #'
-#' `graph_from_incidence_matrix()` can operate in two modes, depending on the
+#' `graph_from_biadjacency_matrix()` can operate in two modes, depending on the
 #' `multiple` argument. If it is `FALSE` then a single edge is
-#' created for every non-zero element in the incidence matrix. If
+#' created for every non-zero element in the bipartite adjacency matrix. If
 #' `multiple` is `TRUE`, then the matrix elements are rounded up to
 #' the closest non-negative integer to get the number of edges to create
 #' between a pair of vertices.
 #'
 #' @aliases graph.incidence
-#' @param incidence The input incidence matrix. It can also be a sparse matrix
+#' @param incidence The input bipartite adjacency matrix. It can also be a sparse matrix
 #'   from the `Matrix` package.
 #' @param directed Logical scalar, whether to create a directed graph.
 #' @param mode A character constant, defines the direction of the edges in
 #'   directed graphs, ignored for undirected graphs. If \sQuote{`out`}, then
 #'   edges go from vertices of the first kind (corresponding to rows in the
-#'   incidence matrix) to vertices of the second kind (columns in the incidence
+#'   bipartite adjacency matrix) to vertices of the second kind (columns in the incidence
 #'   matrix). If \sQuote{`in`}, then the opposite direction is used. If
 #'   \sQuote{`all`} or \sQuote{`total`}, then mutual edges are created.
 #' @param multiple Logical scalar, specifies how to interpret the matrix
 #'   elements. See details below.
 #' @param weighted This argument specifies whether to create a weighted graph
-#'   from the incidence matrix. If it is `NULL` then an unweighted graph is
+#'   from the bipartite adjacency matrix. If it is `NULL` then an unweighted graph is
 #'   created and the `multiple` argument is used to determine the edges of
 #'   the graph. If it is a character constant then for every non-zero matrix
 #'   entry an edge is created and the value of the entry is added as an edge
@@ -174,9 +174,9 @@ graph.incidence.dense <- function(incidence, directed, mode, multiple,
 #'   weighted graph is created and the name of the edge attribute will be
 #'   \sQuote{`weight`}.
 #' @param add.names A character constant, `NA` or `NULL`.
-#'   `graph_from_incidence_matrix()` can add the row and column names of the incidence
+#'   `graph_from_biadjacency_matrix()` can add the row and column names of the incidence
 #'   matrix as vertex attributes. If this argument is `NULL` (the default)
-#'   and the incidence matrix has both row and column names, then these are added
+#'   and the bipartite adjacency matrix has both row and column names, then these are added
 #'   as the \sQuote{`name`} vertex attribute. If you want a different vertex
 #'   attribute for this, then give the name of the attributes as a character
 #'   string. If this argument is `NA`, then no vertex attributes (other than
@@ -192,10 +192,15 @@ graph.incidence.dense <- function(incidence, directed, mode, multiple,
 #' inc <- matrix(sample(0:1, 15, repl = TRUE), 3, 5)
 #' colnames(inc) <- letters[1:5]
 #' rownames(inc) <- LETTERS[1:3]
-#' graph_from_incidence_matrix(inc)
+#' graph_from_biadjacency_matrix(inc)
 #'
+#' @details
+#' Some authors refer to the bipartite adjacency matrix as the
+#' "bipartite incidence matrix". igraph 1.6.0 and later does not use
+#' this naming to avoid confusion with the edge-vertex incidence matrix.
+#' @family biadjacency
 #' @export
-graph_from_incidence_matrix <- function(incidence, directed = FALSE,
+graph_from_biadjacency_matrix <- function(incidence, directed = FALSE,
                                         mode = c("all", "out", "in", "total"),
                                         multiple = FALSE, weighted = NULL,
                                         add.names = NULL) {
@@ -243,9 +248,39 @@ graph_from_incidence_matrix <- function(incidence, directed = FALSE,
   }
   res
 }
-
-#' @rdname graph_from_incidence_matrix
-#' @param ... Passed to `graph_from_incidence_matrix()`.
-#' @family incidence
+#' Graph from incidence matrix
+#'
+#' @description
+#' `r lifecycle::badge("deprecated")`
+#'
+#' `graph_from_incidence_matrix()` was renamed to `graph_from_biadjacency_matrix()` to create a more
+#' consistent API.
+#' @inheritParams graph_from_biadjacency_matrix
+#' @keywords internal
+#' @details
+#' Some authors refer to the bipartite adjacency matrix as the
+#' "bipartite incidence matrix". igraph 1.6.0 and later does not use
+#' this naming to avoid confusion with the edge-vertex incidence matrix.
+#' @export
+from_incidence_matrix <- function(...) { # nocov start
+   lifecycle::deprecate_soft("1.6.0", "graph_from_incidence_matrix()", "graph_from_biadjacency_matrix()")
+   graph_from_biadjacency_matrix(...)
+} # nocov end
+#' From incidence matrix
+#'
+#' @description
+#' `r lifecycle::badge("deprecated")`
+#'
+#' `graph_from_incidence_matrix()` was renamed to `graph_from_biadjacency_matrix()` to create a more
+#' consistent API.
+#' @inheritParams graph_from_biadjacency_matrix
+#' @keywords internal
+#' @details
+#' Some authors refer to the bipartite adjacency matrix as the
+#' "bipartite incidence matrix". igraph 1.6.0 and later does not use
+#' this naming to avoid confusion with the edge-vertex incidence matrix.
 #' @export
-from_incidence_matrix <- function(...) constructor_spec(graph_from_incidence_matrix, ...)
+graph_from_incidence_matrix <- function(...) { # nocov start
+   lifecycle::deprecate_soft("1.6.0", "graph_from_incidence_matrix()", "graph_from_biadjacency_matrix()")
+   graph_from_biadjacency_matrix(...)
+} # nocov end
diff --git a/R/layout.R b/R/layout.R
index f20292a7fb5..15b9973ccca 100644
--- a/R/layout.R
+++ b/R/layout.R
@@ -270,7 +270,7 @@ normalize <- function(xmin = -1, xmax = 1, ymin = xmin, ymax = xmax,
 #' @examples
 #' # Random bipartite graph
 #' inc <- matrix(sample(0:1, 50, replace = TRUE, prob = c(2, 1)), 10, 5)
-#' g <- graph_from_incidence_matrix(inc)
+#' g <- graph_from_biadjacency_matrix(inc)
 #' plot(g,
 #'   layout = layout_as_bipartite,
 #'   vertex.color = c("green", "cyan")[V(g)$type + 1]
diff --git a/R/zzz-deprecate.R b/R/zzz-deprecate.R
index 54785c00651..c950fc3300c 100644
--- a/R/zzz-deprecate.R
+++ b/R/zzz-deprecate.R
@@ -184,7 +184,7 @@ deprecated("get.edgelist", as_edgelist)
 #' @export get.graph.attribute
 deprecated("get.graph.attribute", graph_attr)
 #' @export get.incidence
-deprecated("get.incidence", as_incidence_matrix)
+deprecated("get.incidence", as_biadjacency_matrix)
 #' @export get.stochastic
 deprecated("get.stochastic", stochastic_matrix)
 #' @export get.vertex.attribute
@@ -244,7 +244,7 @@ deprecated("graph.full.citation", make_full_citation_graph)
 #' @export graph.graphdb
 deprecated("graph.graphdb", graph_from_graphdb)
 #' @export graph.incidence
-deprecated("graph.incidence", graph_from_incidence_matrix)
+deprecated("graph.incidence", graph_from_biadjacency_matrix)
 #' @export graph.isocreate
 deprecated("graph.isocreate", graph_from_isomorphism_class)
 #' @export graph.kautz
diff --git a/_pkgdown.yml b/_pkgdown.yml
index d80863f9f4d..8e0cd4fb4a2 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -138,7 +138,7 @@ reference:
 - subtitle: Bipartite graphs
 - contents:
   - has_concept("bipartite")
-  - has_concept("incidence")
+  - has_concept("biadjacency")
 - subtitle: Efficiency
 - contents:
   - has_concept("efficiency")
diff --git a/man/as.directed.Rd b/man/as.directed.Rd
index f98074fa198..6da3a446a71 100644
--- a/man/as.directed.Rd
+++ b/man/as.directed.Rd
@@ -105,9 +105,10 @@ Other conversion:
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
diff --git a/man/as.matrix.igraph.Rd b/man/as.matrix.igraph.Rd
index f29e9b74bf7..7c55a76cc05 100644
--- a/man/as.matrix.igraph.Rd
+++ b/man/as.matrix.igraph.Rd
@@ -50,9 +50,10 @@ Other conversion:
 \code{\link{as.directed}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
diff --git a/man/as_adj_list.Rd b/man/as_adj_list.Rd
index 0cbf6432654..c71f8989f61 100644
--- a/man/as_adj_list.Rd
+++ b/man/as_adj_list.Rd
@@ -71,9 +71,10 @@ Other conversion:
 \code{\link{as.directed}()},
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
diff --git a/man/as_adjacency_matrix.Rd b/man/as_adjacency_matrix.Rd
index 1fd13478551..46835075049 100644
--- a/man/as_adjacency_matrix.Rd
+++ b/man/as_adjacency_matrix.Rd
@@ -87,9 +87,10 @@ Other conversion:
 \code{\link{as.directed}()},
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
diff --git a/man/as_biadjacency_matrix.Rd b/man/as_biadjacency_matrix.Rd
new file mode 100644
index 00000000000..18e27092556
--- /dev/null
+++ b/man/as_biadjacency_matrix.Rd
@@ -0,0 +1,81 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/conversion.R
+\name{as_biadjacency_matrix}
+\alias{as_biadjacency_matrix}
+\alias{get.incidence}
+\title{Bipartite adjacency matrix of a bipartite graph}
+\usage{
+as_biadjacency_matrix(
+  graph,
+  types = NULL,
+  attr = NULL,
+  names = TRUE,
+  sparse = FALSE
+)
+}
+\arguments{
+\item{graph}{The input graph. The direction of the edges is ignored in
+directed graphs.}
+
+\item{types}{An optional vertex type vector to use instead of the
+\code{type} vertex attribute. You must supply this argument if the graph has
+no \code{type} vertex attribute.}
+
+\item{attr}{Either \code{NULL} or a character string giving an edge
+attribute name. If \code{NULL}, then a traditional bipartite adjacency matrix is
+returned. If not \code{NULL} then the values of the given edge attribute are
+included in the bipartite adjacency matrix. If the graph has multiple edges, the edge
+attribute of an arbitrarily chosen edge (for the multiple edges) is
+included.}
+
+\item{names}{Logical scalar, if \code{TRUE} and the vertices in the graph
+are named (i.e. the graph has a vertex attribute called \code{name}), then
+vertex names will be added to the result as row and column names. Otherwise
+the ids of the vertices are used as row and column names.}
+
+\item{sparse}{Logical scalar, if it is \code{TRUE} then a sparse matrix is
+created, you will need the \code{Matrix} package for this.}
+}
+\value{
+A sparse or dense matrix.
+}
+\description{
+This function can return a sparse or dense bipartite adjacency matrix of a bipartite
+network. The bipartite adjacency matrix is an \eqn{n} times \eqn{m} matrix, \eqn{n}
+and \eqn{m} are the number of vertices of the two kinds.
+}
+\details{
+Bipartite graphs have a \code{type} vertex attribute in igraph, this is
+boolean and \code{FALSE} for the vertices of the first kind and \code{TRUE}
+for vertices of the second kind.
+
+Some authors refer to the bipartite adjacency matrix as the
+"bipartite incidence matrix". igraph 1.6.0 and later does not use
+this naming to avoid confusion with the edge-vertex incidence matrix.
+}
+\examples{
+
+g <- make_bipartite_graph(c(0, 1, 0, 1, 0, 0), c(1, 2, 2, 3, 3, 4))
+as_biadjacency_matrix(g)
+
+}
+\seealso{
+\code{\link[=graph_from_biadjacency_matrix]{graph_from_biadjacency_matrix()}} for the opposite operation.
+
+Other conversion: 
+\code{\link{as.directed}()},
+\code{\link{as.matrix.igraph}()},
+\code{\link{as_adj_list}()},
+\code{\link{as_adjacency_matrix}()},
+\code{\link{as_data_frame}()},
+\code{\link{as_edgelist}()},
+\code{\link{as_graphnel}()},
+\code{\link{as_long_data_frame}()},
+\code{\link{graph_from_adj_list}()},
+\code{\link{graph_from_graphnel}()}
+}
+\author{
+Gabor Csardi \email{csardi.gabor@gmail.com}
+}
+\concept{conversion}
+\keyword{graphs}
diff --git a/man/as_edgelist.Rd b/man/as_edgelist.Rd
index 221e3147808..2a62c68e448 100644
--- a/man/as_edgelist.Rd
+++ b/man/as_edgelist.Rd
@@ -41,8 +41,9 @@ Other conversion:
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
diff --git a/man/as_graphnel.Rd b/man/as_graphnel.Rd
index 89aed16b28b..53d9a5f1b8c 100644
--- a/man/as_graphnel.Rd
+++ b/man/as_graphnel.Rd
@@ -53,8 +53,9 @@ Other conversion:
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
diff --git a/man/as_incidence_matrix.Rd b/man/as_incidence_matrix.Rd
index 316927fbc14..50c68cb715c 100644
--- a/man/as_incidence_matrix.Rd
+++ b/man/as_incidence_matrix.Rd
@@ -2,75 +2,19 @@
 % Please edit documentation in R/conversion.R
 \name{as_incidence_matrix}
 \alias{as_incidence_matrix}
-\alias{get.incidence}
-\title{Incidence matrix of a bipartite graph}
+\title{As incidence matrix}
 \usage{
-as_incidence_matrix(
-  graph,
-  types = NULL,
-  attr = NULL,
-  names = TRUE,
-  sparse = FALSE
-)
-}
-\arguments{
-\item{graph}{The input graph. The direction of the edges is ignored in
-directed graphs.}
-
-\item{types}{An optional vertex type vector to use instead of the
-\code{type} vertex attribute. You must supply this argument if the graph has
-no \code{type} vertex attribute.}
-
-\item{attr}{Either \code{NULL} or a character string giving an edge
-attribute name. If \code{NULL}, then a traditional incidence matrix is
-returned. If not \code{NULL} then the values of the given edge attribute are
-included in the incidence matrix. If the graph has multiple edges, the edge
-attribute of an arbitrarily chosen edge (for the multiple edges) is
-included.}
-
-\item{names}{Logical scalar, if \code{TRUE} and the vertices in the graph
-are named (i.e. the graph has a vertex attribute called \code{name}), then
-vertex names will be added to the result as row and column names. Otherwise
-the ids of the vertices are used as row and column names.}
-
-\item{sparse}{Logical scalar, if it is \code{TRUE} then a sparse matrix is
-created, you will need the \code{Matrix} package for this.}
-}
-\value{
-A sparse or dense matrix.
+as_incidence_matrix(...)
 }
 \description{
-This function can return a sparse or dense incidence matrix of a bipartite
-network. The incidence matrix is an \eqn{n} times \eqn{m} matrix, \eqn{n}
-and \eqn{m} are the number of vertices of the two kinds.
-}
-\details{
-Bipartite graphs have a \code{type} vertex attribute in igraph, this is
-boolean and \code{FALSE} for the vertices of the first kind and \code{TRUE}
-for vertices of the second kind.
-}
-\examples{
-
-g <- make_bipartite_graph(c(0, 1, 0, 1, 0, 0), c(1, 2, 2, 3, 3, 4))
-as_incidence_matrix(g)
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
 
+\code{as_incidence_matrix()} was renamed to \code{as_biadjacency_matrix()} to create a more
+consistent API.
 }
-\seealso{
-\code{\link[=graph_from_incidence_matrix]{graph_from_incidence_matrix()}} for the opposite operation.
-
-Other conversion: 
-\code{\link{as.directed}()},
-\code{\link{as.matrix.igraph}()},
-\code{\link{as_adj_list}()},
-\code{\link{as_adjacency_matrix}()},
-\code{\link{as_edgelist}()},
-\code{\link{as_graphnel}()},
-\code{\link{as_long_data_frame}()},
-\code{\link{graph_from_adj_list}()},
-\code{\link{graph_from_graphnel}()}
-}
-\author{
-Gabor Csardi \email{csardi.gabor@gmail.com}
+\details{
+Some authors refer to the bipartite adjacency matrix as the
+"bipartite incidence matrix". igraph 1.6.0 and later does not use
+this naming to avoid confusion with the edge-vertex incidence matrix.
 }
-\concept{conversion}
-\keyword{graphs}
+\keyword{internal}
diff --git a/man/as_long_data_frame.Rd b/man/as_long_data_frame.Rd
index 045afcd8617..053e8077b5c 100644
--- a/man/as_long_data_frame.Rd
+++ b/man/as_long_data_frame.Rd
@@ -36,9 +36,10 @@ Other conversion:
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{graph_from_adj_list}()},
 \code{\link{graph_from_graphnel}()}
 }
diff --git a/man/bipartite_projection.Rd b/man/bipartite_projection.Rd
index bf17251d8b8..4e90535cef1 100644
--- a/man/bipartite_projection.Rd
+++ b/man/bipartite_projection.Rd
@@ -84,7 +84,7 @@ rownames(M) <- c("Alice", "Bob", "Cecil", "Dan", "Ethel")
 colnames(M) <- c("Party", "Skiing", "Badminton")
 M[] <- sample(0:1, length(M), replace = TRUE)
 M
-g2 <- graph_from_incidence_matrix(M)
+g2 <- graph_from_biadjacency_matrix(M)
 g2$name <- "Event network"
 proj2 <- bipartite_projection(g2)
 print(proj2[[1]], g = TRUE, e = TRUE)
diff --git a/man/from_incidence_matrix.Rd b/man/from_incidence_matrix.Rd
new file mode 100644
index 00000000000..4b54c6d6160
--- /dev/null
+++ b/man/from_incidence_matrix.Rd
@@ -0,0 +1,20 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/incidence.R
+\name{from_incidence_matrix}
+\alias{from_incidence_matrix}
+\title{Graph from incidence matrix}
+\usage{
+from_incidence_matrix(...)
+}
+\description{
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
+
+\code{graph_from_incidence_matrix()} was renamed to \code{graph_from_biadjacency_matrix()} to create a more
+consistent API.
+}
+\details{
+Some authors refer to the bipartite adjacency matrix as the
+"bipartite incidence matrix". igraph 1.6.0 and later does not use
+this naming to avoid confusion with the edge-vertex incidence matrix.
+}
+\keyword{internal}
diff --git a/man/graph_from_adj_list.Rd b/man/graph_from_adj_list.Rd
index 4e72b5fcb2e..21ecdb70ebc 100644
--- a/man/graph_from_adj_list.Rd
+++ b/man/graph_from_adj_list.Rd
@@ -71,9 +71,10 @@ Other conversion:
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_graphnel}()}
 }
diff --git a/man/graph_from_biadjacency_matrix.Rd b/man/graph_from_biadjacency_matrix.Rd
new file mode 100644
index 00000000000..3f4874ead70
--- /dev/null
+++ b/man/graph_from_biadjacency_matrix.Rd
@@ -0,0 +1,94 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/incidence.R
+\name{graph_from_biadjacency_matrix}
+\alias{graph_from_biadjacency_matrix}
+\alias{graph.incidence}
+\title{Create graphs from a bipartite adjacency matrix}
+\usage{
+graph_from_biadjacency_matrix(
+  incidence,
+  directed = FALSE,
+  mode = c("all", "out", "in", "total"),
+  multiple = FALSE,
+  weighted = NULL,
+  add.names = NULL
+)
+}
+\arguments{
+\item{incidence}{The input bipartite adjacency matrix. It can also be a sparse matrix
+from the \code{Matrix} package.}
+
+\item{directed}{Logical scalar, whether to create a directed graph.}
+
+\item{mode}{A character constant, defines the direction of the edges in
+directed graphs, ignored for undirected graphs. If \sQuote{\code{out}}, then
+edges go from vertices of the first kind (corresponding to rows in the
+bipartite adjacency matrix) to vertices of the second kind (columns in the incidence
+matrix). If \sQuote{\verb{in}}, then the opposite direction is used. If
+\sQuote{\code{all}} or \sQuote{\code{total}}, then mutual edges are created.}
+
+\item{multiple}{Logical scalar, specifies how to interpret the matrix
+elements. See details below.}
+
+\item{weighted}{This argument specifies whether to create a weighted graph
+from the bipartite adjacency matrix. If it is \code{NULL} then an unweighted graph is
+created and the \code{multiple} argument is used to determine the edges of
+the graph. If it is a character constant then for every non-zero matrix
+entry an edge is created and the value of the entry is added as an edge
+attribute named by the \code{weighted} argument. If it is \code{TRUE} then a
+weighted graph is created and the name of the edge attribute will be
+\sQuote{\code{weight}}.}
+
+\item{add.names}{A character constant, \code{NA} or \code{NULL}.
+\code{graph_from_biadjacency_matrix()} can add the row and column names of the incidence
+matrix as vertex attributes. If this argument is \code{NULL} (the default)
+and the bipartite adjacency matrix has both row and column names, then these are added
+as the \sQuote{\code{name}} vertex attribute. If you want a different vertex
+attribute for this, then give the name of the attributes as a character
+string. If this argument is \code{NA}, then no vertex attributes (other than
+type) will be added.}
+}
+\value{
+A bipartite igraph graph. In other words, an igraph graph that has a
+vertex attribute \code{type}.
+}
+\description{
+\code{graph_from_biadjacency_matrix()} creates a bipartite igraph graph from an incidence
+matrix.
+}
+\details{
+Bipartite graphs have a \sQuote{\code{type}} vertex attribute in igraph,
+this is boolean and \code{FALSE} for the vertices of the first kind and
+\code{TRUE} for vertices of the second kind.
+
+\code{graph_from_biadjacency_matrix()} can operate in two modes, depending on the
+\code{multiple} argument. If it is \code{FALSE} then a single edge is
+created for every non-zero element in the bipartite adjacency matrix. If
+\code{multiple} is \code{TRUE}, then the matrix elements are rounded up to
+the closest non-negative integer to get the number of edges to create
+between a pair of vertices.
+
+Some authors refer to the bipartite adjacency matrix as the
+"bipartite incidence matrix". igraph 1.6.0 and later does not use
+this naming to avoid confusion with the edge-vertex incidence matrix.
+}
+\examples{
+
+inc <- matrix(sample(0:1, 15, repl = TRUE), 3, 5)
+colnames(inc) <- letters[1:5]
+rownames(inc) <- LETTERS[1:3]
+graph_from_biadjacency_matrix(inc)
+
+}
+\seealso{
+\code{\link[=make_bipartite_graph]{make_bipartite_graph()}} for another way to create bipartite
+graphs
+
+Other biadjacency: 
+\code{\link{as_data_frame}()}
+}
+\author{
+Gabor Csardi \email{csardi.gabor@gmail.com}
+}
+\concept{biadjacency}
+\keyword{graphs}
diff --git a/man/graph_from_data_frame.Rd b/man/graph_from_data_frame.Rd
index ea3c4706f6d..4f7c66b9fa4 100644
--- a/man/graph_from_data_frame.Rd
+++ b/man/graph_from_data_frame.Rd
@@ -129,8 +129,25 @@ as_data_frame(g, what = "edges")
 \code{\link[=graph_from_literal]{graph_from_literal()}}
 for another way to create graphs, \code{\link[=read.table]{read.table()}} to read in tables
 from files.
+
+Other conversion: 
+\code{\link{as.directed}()},
+\code{\link{as.matrix.igraph}()},
+\code{\link{as_adj_list}()},
+\code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_edgelist}()},
+\code{\link{as_graphnel}()},
+\code{\link{as_long_data_frame}()},
+\code{\link{graph_from_adj_list}()},
+\code{\link{graph_from_graphnel}()}
+
+Other biadjacency: 
+\code{\link{graph_from_biadjacency_matrix}()}
 }
 \author{
 Gabor Csardi \email{csardi.gabor@gmail.com}
 }
+\concept{biadjacency}
+\concept{conversion}
 \keyword{graphs}
diff --git a/man/graph_from_graphnel.Rd b/man/graph_from_graphnel.Rd
index 6b01472dda3..0dfc1dd48e9 100644
--- a/man/graph_from_graphnel.Rd
+++ b/man/graph_from_graphnel.Rd
@@ -67,9 +67,10 @@ Other conversion:
 \code{\link{as.matrix.igraph}()},
 \code{\link{as_adj_list}()},
 \code{\link{as_adjacency_matrix}()},
+\code{\link{as_biadjacency_matrix}()},
+\code{\link{as_data_frame}()},
 \code{\link{as_edgelist}()},
 \code{\link{as_graphnel}()},
-\code{\link{as_incidence_matrix}()},
 \code{\link{as_long_data_frame}()},
 \code{\link{graph_from_adj_list}()}
 }
diff --git a/man/graph_from_incidence_matrix.Rd b/man/graph_from_incidence_matrix.Rd
index 6efcf24146e..c7f6cf1df15 100644
--- a/man/graph_from_incidence_matrix.Rd
+++ b/man/graph_from_incidence_matrix.Rd
@@ -2,91 +2,19 @@
 % Please edit documentation in R/incidence.R
 \name{graph_from_incidence_matrix}
 \alias{graph_from_incidence_matrix}
-\alias{graph.incidence}
-\alias{from_incidence_matrix}
-\title{Create graphs from an incidence matrix}
+\title{From incidence matrix}
 \usage{
-graph_from_incidence_matrix(
-  incidence,
-  directed = FALSE,
-  mode = c("all", "out", "in", "total"),
-  multiple = FALSE,
-  weighted = NULL,
-  add.names = NULL
-)
-
-from_incidence_matrix(...)
-}
-\arguments{
-\item{incidence}{The input incidence matrix. It can also be a sparse matrix
-from the \code{Matrix} package.}
-
-\item{directed}{Logical scalar, whether to create a directed graph.}
-
-\item{mode}{A character constant, defines the direction of the edges in
-directed graphs, ignored for undirected graphs. If \sQuote{\code{out}}, then
-edges go from vertices of the first kind (corresponding to rows in the
-incidence matrix) to vertices of the second kind (columns in the incidence
-matrix). If \sQuote{\verb{in}}, then the opposite direction is used. If
-\sQuote{\code{all}} or \sQuote{\code{total}}, then mutual edges are created.}
-
-\item{multiple}{Logical scalar, specifies how to interpret the matrix
-elements. See details below.}
-
-\item{weighted}{This argument specifies whether to create a weighted graph
-from the incidence matrix. If it is \code{NULL} then an unweighted graph is
-created and the \code{multiple} argument is used to determine the edges of
-the graph. If it is a character constant then for every non-zero matrix
-entry an edge is created and the value of the entry is added as an edge
-attribute named by the \code{weighted} argument. If it is \code{TRUE} then a
-weighted graph is created and the name of the edge attribute will be
-\sQuote{\code{weight}}.}
-
-\item{add.names}{A character constant, \code{NA} or \code{NULL}.
-\code{graph_from_incidence_matrix()} can add the row and column names of the incidence
-matrix as vertex attributes. If this argument is \code{NULL} (the default)
-and the incidence matrix has both row and column names, then these are added
-as the \sQuote{\code{name}} vertex attribute. If you want a different vertex
-attribute for this, then give the name of the attributes as a character
-string. If this argument is \code{NA}, then no vertex attributes (other than
-type) will be added.}
-
-\item{...}{Passed to \code{graph_from_incidence_matrix()}.}
-}
-\value{
-A bipartite igraph graph. In other words, an igraph graph that has a
-vertex attribute \code{type}.
+graph_from_incidence_matrix(...)
 }
 \description{
-\code{graph_from_incidence_matrix()} creates a bipartite igraph graph from an incidence
-matrix.
-}
-\details{
-Bipartite graphs have a \sQuote{\code{type}} vertex attribute in igraph,
-this is boolean and \code{FALSE} for the vertices of the first kind and
-\code{TRUE} for vertices of the second kind.
-
-\code{graph_from_incidence_matrix()} can operate in two modes, depending on the
-\code{multiple} argument. If it is \code{FALSE} then a single edge is
-created for every non-zero element in the incidence matrix. If
-\code{multiple} is \code{TRUE}, then the matrix elements are rounded up to
-the closest non-negative integer to get the number of edges to create
-between a pair of vertices.
-}
-\examples{
-
-inc <- matrix(sample(0:1, 15, repl = TRUE), 3, 5)
-colnames(inc) <- letters[1:5]
-rownames(inc) <- LETTERS[1:3]
-graph_from_incidence_matrix(inc)
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
 
+\code{graph_from_incidence_matrix()} was renamed to \code{graph_from_biadjacency_matrix()} to create a more
+consistent API.
 }
-\seealso{
-\code{\link[=make_bipartite_graph]{make_bipartite_graph()}} for another way to create bipartite
-graphs
-}
-\author{
-Gabor Csardi \email{csardi.gabor@gmail.com}
+\details{
+Some authors refer to the bipartite adjacency matrix as the
+"bipartite incidence matrix". igraph 1.6.0 and later does not use
+this naming to avoid confusion with the edge-vertex incidence matrix.
 }
-\concept{incidence}
-\keyword{graphs}
+\keyword{internal}
diff --git a/man/layout_as_bipartite.Rd b/man/layout_as_bipartite.Rd
index 4d900726f77..b4853a2809d 100644
--- a/man/layout_as_bipartite.Rd
+++ b/man/layout_as_bipartite.Rd
@@ -47,7 +47,7 @@ edge crossings, using the Sugiyama algorithm (see
 \examples{
 # Random bipartite graph
 inc <- matrix(sample(0:1, 50, replace = TRUE, prob = c(2, 1)), 10, 5)
-g <- graph_from_incidence_matrix(inc)
+g <- graph_from_biadjacency_matrix(inc)
 plot(g,
   layout = layout_as_bipartite,
   vertex.color = c("green", "cyan")[V(g)$type + 1]
diff --git a/tests/testthat/_snaps/graph.adjacency.md b/tests/testthat/_snaps/graph.adjacency.md
index 301f8d84952..c46c4146288 100644
--- a/tests/testthat/_snaps/graph.adjacency.md
+++ b/tests/testthat/_snaps/graph.adjacency.md
@@ -21,7 +21,7 @@
       graph_from_adjacency_matrix(m, mode = "undirected")
     Condition
       Warning:
-      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.5.2.
+      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.6.0.
       i Use mode = "max" to achieve the original behavior.
     Output
       IGRAPH U--- 2 2 -- 
@@ -53,7 +53,7 @@
       graph_from_adjacency_matrix(m2, mode = "undirected")
     Condition
       Warning:
-      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.5.2.
+      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.6.0.
       i Use mode = "max" to achieve the original behavior.
     Output
       IGRAPH U--- 2 0 -- 
@@ -62,7 +62,7 @@
       graph_from_adjacency_matrix(1)
     Condition
       Warning:
-      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be a matrix as of igraph 1.5.2.
+      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be a matrix as of igraph 1.6.0.
     Output
       IGRAPH D--- 1 1 -- 
       + edge:
@@ -71,7 +71,7 @@
       graph_from_adjacency_matrix(1, mode = "undirected")
     Condition
       Warning:
-      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be a matrix as of igraph 1.5.2.
+      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be a matrix as of igraph 1.6.0.
     Output
       IGRAPH U--- 1 1 -- 
       + edge:
@@ -101,7 +101,7 @@
       graph_from_adjacency_matrix(m, mode = "undirected")
     Condition
       Warning:
-      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.5.2.
+      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.6.0.
       i Use mode = "max" to achieve the original behavior.
     Output
       IGRAPH U--- 2 2 -- 
@@ -133,7 +133,7 @@
       graph_from_adjacency_matrix(m2, mode = "undirected")
     Condition
       Warning:
-      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.5.2.
+      The `adjmatrix` argument of `graph_from_adjacency_matrix()` must be symmetric with mode = "undirected" as of igraph 1.6.0.
       i Use mode = "max" to achieve the original behavior.
     Output
       IGRAPH U--- 2 0 -- 
diff --git a/tests/testthat/test-bipartite.projection.R b/tests/testthat/test-bipartite.projection.R
index 9ec2a8abcc7..27b039aac3c 100644
--- a/tests/testthat/test-bipartite.projection.R
+++ b/tests/testthat/test-bipartite.projection.R
@@ -12,7 +12,7 @@ test_that("bipartite_projection works", {
   colnames(M) <- c("Party", "Skiing", "Badminton")
   M[] <- sample(0:1, length(M), replace = TRUE)
   M
-  g2 <- graph_from_incidence_matrix(M)
+  g2 <- graph_from_biadjacency_matrix(M)
   expect_that(as.matrix(g2[1:5, 6:8]), equals(M))
   expect_that(as.matrix(g2[1:5, 1:5]), is_equivalent_to(matrix(0, 5, 5)))
   expect_that(as.matrix(g2[6:8, 6:8]), is_equivalent_to(matrix(0, 3, 3)))
diff --git a/tests/testthat/test-get.incidence.R b/tests/testthat/test-get.incidence.R
index 36fb800950d..b4f820dfdee 100644
--- a/tests/testthat/test-get.incidence.R
+++ b/tests/testthat/test-get.incidence.R
@@ -1,15 +1,15 @@
-test_that("as_incidence_matrix works", {
+test_that("as_biadjacency_matrix works", {
   ## Dense
   I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_incidence_matrix(I)
-  I2 <- as_incidence_matrix(g)
+  g <- graph_from_biadjacency_matrix(I)
+  I2 <- as_biadjacency_matrix(g)
   expect_that(I, is_equivalent_to(I2))
   expect_that(rownames(I2), equals(as.character(1:7)))
   expect_that(colnames(I2), equals(as.character(8:12)))
 
   ## Sparse
 
-  I3 <- as_incidence_matrix(g, sparse = TRUE)
+  I3 <- as_biadjacency_matrix(g, sparse = TRUE)
   expect_that(as.matrix(I3), is_equivalent_to(I))
   expect_that(rownames(I3), equals(as.character(1:7)))
   expect_that(colnames(I3), equals(as.character(8:12)))
diff --git a/tests/testthat/test-graph.bipartite.R b/tests/testthat/test-graph.bipartite.R
index 19b60b76f19..8b2c09d9b54 100644
--- a/tests/testthat/test-graph.bipartite.R
+++ b/tests/testthat/test-graph.bipartite.R
@@ -1,6 +1,6 @@
 test_that("make_bipartite_graph works", {
   I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_incidence_matrix(I)
+  g <- graph_from_biadjacency_matrix(I)
 
   edges <- unlist(sapply(seq_len(nrow(I)), function(x) {
     w <- which(I[x, ] != 0) + nrow(I)
@@ -11,7 +11,7 @@ test_that("make_bipartite_graph works", {
     }
   }))
   g2 <- make_bipartite_graph(seq_len(nrow(I) + ncol(I)) > nrow(I), edges)
-  I2 <- as_incidence_matrix(g2)
+  I2 <- as_biadjacency_matrix(g2)
 
   expect_that(I2, is_equivalent_to(I))
 })
diff --git a/tests/testthat/test-is.bipartite.R b/tests/testthat/test-is.bipartite.R
index 47679e884ed..0d0015a4fc3 100644
--- a/tests/testthat/test-is.bipartite.R
+++ b/tests/testthat/test-is.bipartite.R
@@ -1,11 +1,11 @@
 test_that("is_bipartite works", {
   I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_incidence_matrix(I)
+  g <- graph_from_biadjacency_matrix(I)
   expect_true(bipartite_mapping(g)$res)
 
   set.seed(42)
   I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_incidence_matrix(I)
+  g <- graph_from_biadjacency_matrix(I)
   expect_that(
     bipartite_mapping(g),
     equals(list(res = TRUE, type = c(rep(FALSE, 7), rep(TRUE, 5))))