diff --git a/RELEASES.md b/RELEASES.md
index 73e1f74..3cd4d14 100644
--- a/RELEASES.md
+++ b/RELEASES.md
@@ -1,5 +1,20 @@
 # Release notes
 
+## Unreleased (2023-XX-XX)
+
+### Added
+
+- `algorithms::ConvexChecker` to check convexity property of subgraphs of `LinkView`s ([#97][])
+
+### Changed
+
+- References to `PortView`s and `LinkView`s also implement the traits ([#94][])
+- `Toposort` now works with any `LinkView` object ([#96][])
+
+  [#94]: https://github.com/CQCL/portgraph/issues/94
+  [#96]: https://github.com/CQCL/portgraph/issues/96
+  [#97]: https://github.com/CQCL/portgraph/issues/97
+
 ## v0.7.1 (2023-07-13)
 
 ### Fixed
diff --git a/benches/bench_main.rs b/benches/bench_main.rs
index 32b87d0..94e10e0 100644
--- a/benches/bench_main.rs
+++ b/benches/bench_main.rs
@@ -7,4 +7,5 @@ criterion_main! {
     benchmarks::hierarchy::benches,
     benchmarks::portgraph::benches,
     benchmarks::toposort::benches,
+    benchmarks::convex::benches,
 }
diff --git a/benches/benchmarks/convex.rs b/benches/benchmarks/convex.rs
new file mode 100644
index 0000000..7daf59f
--- /dev/null
+++ b/benches/benchmarks/convex.rs
@@ -0,0 +1,47 @@
+use criterion::{black_box, criterion_group, AxisScale, BenchmarkId, Criterion, PlotConfiguration};
+use portgraph::{algorithms::ConvexChecker, PortView};
+
+use super::generators::make_two_track_dag;
+
+fn bench_convex_construction(c: &mut Criterion) {
+    let mut g = c.benchmark_group("initialize convex checker object");
+    g.plot_config(PlotConfiguration::default().summary_scale(AxisScale::Logarithmic));
+
+    for size in [100, 1_000, 10_000] {
+        g.bench_with_input(
+            BenchmarkId::new("initalize_convexity", size),
+            &size,
+            |b, size| {
+                let graph = make_two_track_dag(*size);
+                b.iter(|| black_box(ConvexChecker::new(&graph)))
+            },
+        );
+    }
+    g.finish();
+}
+
+/// We benchmark the worst case scenario, where the "subgraph" is the
+/// entire graph itself.
+fn bench_convex(c: &mut Criterion) {
+    let mut g = c.benchmark_group("Runtime convexity check");
+    g.plot_config(PlotConfiguration::default().summary_scale(AxisScale::Logarithmic));
+
+    for size in [100, 1_000, 10_000] {
+        let graph = make_two_track_dag(size);
+        let mut checker = ConvexChecker::new(&graph);
+        g.bench_with_input(
+            BenchmarkId::new("check_convexity", size),
+            &size,
+            |b, _size| b.iter(|| black_box(checker.is_node_convex(graph.nodes_iter()))),
+        );
+    }
+    g.finish();
+}
+
+criterion_group! {
+    name = benches;
+    config = Criterion::default();
+    targets =
+        bench_convex,
+        bench_convex_construction
+}
diff --git a/benches/benchmarks/mod.rs b/benches/benchmarks/mod.rs
index 2682cb9..6664f76 100644
--- a/benches/benchmarks/mod.rs
+++ b/benches/benchmarks/mod.rs
@@ -1,5 +1,6 @@
 pub mod generators;
 
+pub mod convex;
 pub mod hierarchy;
 pub mod portgraph;
 pub mod toposort;
diff --git a/src/algorithms.rs b/src/algorithms.rs
index 6c52858..cd15b75 100644
--- a/src/algorithms.rs
+++ b/src/algorithms.rs
@@ -1,9 +1,11 @@
 //! Algorithm implementations for portgraphs.
 
+mod convex;
 mod dominators;
 mod post_order;
 mod toposort;
 
+pub use convex::ConvexChecker;
 pub use dominators::{dominators, dominators_filtered, DominatorTree};
 pub use post_order::{postorder, postorder_filtered, PostOrder};
 pub use toposort::{toposort, toposort_filtered, TopoSort};
diff --git a/src/algorithms/convex.rs b/src/algorithms/convex.rs
new file mode 100644
index 0000000..d4bd75c
--- /dev/null
+++ b/src/algorithms/convex.rs
@@ -0,0 +1,288 @@
+//! Convexity checking for portgraphs.
+//!
+//! This is based on a [`ConvexChecker`] object that is expensive to create
+//! (linear in the size of the graph), but can be reused to check multiple
+//! subgraphs for convexity quickly.
+
+use std::collections::BTreeSet;
+
+use bitvec::bitvec;
+use bitvec::vec::BitVec;
+
+use crate::algorithms::toposort;
+use crate::{Direction, LinkView, NodeIndex, PortIndex, SecondaryMap, UnmanagedDenseMap};
+
+use super::TopoSort;
+
+/// A pre-computed datastructure for fast convexity checking.
+pub struct ConvexChecker<G> {
+    graph: G,
+    // The nodes in topological order
+    topsort_nodes: Vec<NodeIndex>,
+    // The index of a node in the topological order (the inverse of topsort_nodes)
+    topsort_ind: UnmanagedDenseMap<NodeIndex, usize>,
+    // A temporary datastructure used during `is_convex`
+    causal: CausalVec,
+}
+
+impl<G> ConvexChecker<G>
+where
+    G: LinkView + Copy,
+{
+    /// Create a new ConvexChecker.
+    pub fn new(graph: G) -> Self {
+        let inputs = graph
+            .nodes_iter()
+            .filter(|&n| graph.input_neighbours(n).count() == 0);
+        let topsort: TopoSort<_> = toposort(graph, inputs, Direction::Outgoing);
+        let topsort_nodes: Vec<_> = topsort.collect();
+        let mut topsort_ind = UnmanagedDenseMap::with_capacity(graph.node_count());
+        for (i, &n) in topsort_nodes.iter().enumerate() {
+            topsort_ind.set(n, i);
+        }
+        let causal = CausalVec::new(topsort_nodes.len());
+        Self {
+            graph,
+            topsort_nodes,
+            topsort_ind,
+            causal,
+        }
+    }
+
+    /// The graph on which convexity queries can be made.
+    pub fn graph(&self) -> G {
+        self.graph
+    }
+
+    /// Whether the subgraph induced by the node set is convex.
+    ///
+    /// An induced subgraph is convex if there is no node that is both in the
+    /// past and in the future of another node of the subgraph.
+    ///
+    /// This function requires mutable access to `self` because it uses a
+    /// temporary datastructure within the object.
+    ///
+    /// ## Arguments
+    ///
+    /// - `nodes`: The nodes inducing a subgraph of `self.graph()`.
+    ///
+    /// ## Algorithm
+    ///
+    /// Each node in the "vicinity" of the subgraph will be assigned a causal
+    /// property, either of being in the past or in the future of the subgraph.
+    /// It can then be checked whether there is a node in the past that is also
+    /// in the future, violating convexity.
+    ///
+    /// Currently, the "vicinity" of a subgraph is defined as the set of nodes
+    /// that are in the interval between the first and last node of the subgraph
+    /// in some topological order. In the worst case this will traverse every
+    /// node in the graph and can be improved on in the future.
+    pub fn is_node_convex(&mut self, nodes: impl IntoIterator<Item = NodeIndex>) -> bool {
+        let nodes: BTreeSet<_> = nodes.into_iter().map(|n| self.topsort_ind[n]).collect();
+        let min_ind = *nodes.first().unwrap();
+        let max_ind = *nodes.last().unwrap();
+        for ind in min_ind..=max_ind {
+            let n = self.topsort_nodes[ind];
+            let mut in_inds = {
+                let in_neighs = self.graph.input_neighbours(n);
+                in_neighs
+                    .map(|n| self.topsort_ind[n])
+                    .filter(|&ind| ind >= min_ind)
+            };
+            if nodes.contains(&ind) {
+                if in_inds.any(|ind| self.causal.get(ind) == Causal::Future) {
+                    // There is a node in the past that is also in the future!
+                    return false;
+                }
+                self.causal.set(ind, Causal::Past);
+            } else {
+                let ind_causal = match in_inds
+                    .any(|ind| nodes.contains(&ind) || self.causal.get(ind) == Causal::Future)
+                {
+                    true => Causal::Future,
+                    false => Causal::Past,
+                };
+                self.causal.set(ind, ind_causal);
+            }
+        }
+        true
+    }
+
+    /// Whether a subgraph is convex.
+    ///
+    /// A subgraph is convex if there is no path between two nodes of the
+    /// sugraph that has an edge outside of the subgraph.
+    ///
+    /// Equivalently, we check the following two conditions:
+    ///  - There is no node that is both in the past and in the future of
+    ///    another node of the subgraph (convexity on induced subgraph),
+    ///  - There is no edge from an output port to an input port.
+    ///
+    /// This function requires mutable access to `self` because it uses a
+    /// temporary datastructure within the object.
+    ///
+    /// ## Arguments
+    ///
+    /// - `nodes`: The nodes of the subgraph of `self.graph`,
+    /// - `inputs`: The input ports of the subgraph of `self.graph`. These must
+    ///   be [`Direction::Incoming`] ports of a node in `nodes`,
+    /// - `outputs`: The output ports of the subgraph of `self.graph`. These
+    ///   must be [`Direction::Outgoing`] ports of a node in `nodes`.
+    ///
+    /// Any edge between two nodes of the subgraph that does not have an explicit
+    /// input or output port is considered within the subgraph.
+    pub fn is_convex(
+        &mut self,
+        nodes: impl IntoIterator<Item = NodeIndex>,
+        inputs: impl IntoIterator<Item = PortIndex>,
+        outputs: impl IntoIterator<Item = PortIndex>,
+    ) -> bool {
+        let pre_outputs: BTreeSet<_> = outputs
+            .into_iter()
+            .filter_map(|p| Some(self.graph.port_link(p)?.into()))
+            .collect();
+        if inputs.into_iter().any(|p| pre_outputs.contains(&p)) {
+            return false;
+        }
+        self.is_node_convex(nodes)
+    }
+}
+
+/// Whether a node is in the past or in the future of a subgraph.
+#[derive(Default, Clone, Debug, PartialEq, Eq)]
+enum Causal {
+    #[default]
+    Past,
+    Future,
+}
+
+/// A memory-efficient substitute for `Vec<Causal>`.
+struct CausalVec(BitVec);
+
+impl From<bool> for Causal {
+    fn from(b: bool) -> Self {
+        match b {
+            true => Self::Future,
+            false => Self::Past,
+        }
+    }
+}
+
+impl From<Causal> for bool {
+    fn from(c: Causal) -> Self {
+        match c {
+            Causal::Past => false,
+            Causal::Future => true,
+        }
+    }
+}
+
+impl CausalVec {
+    fn new(len: usize) -> Self {
+        Self(bitvec![0; len])
+    }
+
+    fn set(&mut self, index: usize, causal: Causal) {
+        self.0.set(index, causal.into());
+    }
+
+    fn get(&self, index: usize) -> Causal {
+        self.0[index].into()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::{LinkMut, NodeIndex, PortGraph, PortMut, PortView};
+
+    use super::ConvexChecker;
+
+    fn graph() -> (PortGraph, [NodeIndex; 7]) {
+        let mut g = PortGraph::new();
+        let i1 = g.add_node(0, 2);
+        let i2 = g.add_node(0, 1);
+        let i3 = g.add_node(0, 1);
+
+        let n1 = g.add_node(2, 2);
+        g.link_nodes(i1, 0, n1, 0).unwrap();
+        g.link_nodes(i2, 0, n1, 1).unwrap();
+
+        let n2 = g.add_node(2, 2);
+        g.link_nodes(i1, 1, n2, 0).unwrap();
+        g.link_nodes(i3, 0, n2, 1).unwrap();
+
+        let o1 = g.add_node(2, 0);
+        g.link_nodes(n1, 0, o1, 0).unwrap();
+        g.link_nodes(n2, 0, o1, 1).unwrap();
+
+        let o2 = g.add_node(2, 0);
+        g.link_nodes(n1, 1, o2, 0).unwrap();
+        g.link_nodes(n2, 1, o2, 1).unwrap();
+
+        (g, [i1, i2, i3, n1, n2, o1, o2])
+    }
+
+    #[test]
+    fn induced_convexity_test() {
+        let (g, [i1, i2, i3, n1, n2, o1, o2]) = graph();
+        let mut checker = ConvexChecker::new(&g);
+
+        assert!(checker.is_node_convex([i1, i2, i3]));
+        assert!(checker.is_node_convex([i1, n2]));
+        assert!(!checker.is_node_convex([i1, n2, o2]));
+        assert!(!checker.is_node_convex([i1, n2, o1]));
+        assert!(checker.is_node_convex([i1, n2, o1, n1]));
+        assert!(checker.is_node_convex([i1, n2, o2, n1]));
+        assert!(checker.is_node_convex([i1, i3, n2]));
+        assert!(!checker.is_node_convex([i1, i3, o2]));
+    }
+
+    #[test]
+    fn edge_convexity_test() {
+        let (g, [i1, i2, _, n1, n2, _, o2]) = graph();
+        let mut checker = ConvexChecker::new(&g);
+
+        assert!(checker.is_convex(
+            [i1, n2],
+            [g.input(n2, 1).unwrap()],
+            [
+                g.output(i1, 0).unwrap(),
+                g.output(n2, 0).unwrap(),
+                g.output(n2, 1).unwrap()
+            ]
+        ));
+
+        assert!(checker.is_convex(
+            [i2, n1, o2],
+            [g.input(n1, 0).unwrap(), g.input(o2, 1).unwrap()],
+            [g.output(n1, 0).unwrap(),]
+        ));
+
+        assert!(!checker.is_convex(
+            [i2, n1, o2],
+            [
+                g.input(n1, 0).unwrap(),
+                g.input(o2, 1).unwrap(),
+                g.input(o2, 0).unwrap()
+            ],
+            [g.output(n1, 0).unwrap(), g.output(n1, 1).unwrap()]
+        ));
+    }
+
+    #[test]
+    fn dangling_input() {
+        let mut g = PortGraph::new();
+        let n = g.add_node(1, 1);
+        let mut checker = ConvexChecker::new(&g);
+        assert!(checker.is_node_convex([n]));
+    }
+
+    #[test]
+    fn disconnected_graph() {
+        let mut g = PortGraph::new();
+        let n = g.add_node(1, 1);
+        g.add_node(1, 1);
+        let mut checker = ConvexChecker::new(&g);
+        assert!(checker.is_node_convex([n]));
+    }
+}