diff --git a/src/models.rs b/src/models.rs
index 9aeb4e5..23a0809 100644
--- a/src/models.rs
+++ b/src/models.rs
@@ -10,7 +10,7 @@ impl From<Vertex> for usize {
 }
 
 #[derive(Copy, Clone, PartialEq, Eq)]
-struct Incidence(usize);
+pub struct Incidence(usize);
 
 struct VertexIncidenceHeader {
     incidence_count: usize,
@@ -69,6 +69,8 @@ impl Graph {
 impl GraphTopology for Graph {
     type Vertex = Vertex;
 
+    type Edge = Incidence;
+
     fn vertex_count(&self) -> usize {
         self.vertices.len()
     }
@@ -104,9 +106,10 @@ impl GraphTopology for Graph {
         Vertex(self.vertices.len() - 1)
     }
 
-    fn add_edge(&mut self, v1: Self::Vertex, v2: Self::Vertex) {
+    fn add_edge(&mut self, v1: Self::Vertex, v2: Self::Vertex) -> Self::Edge {
         self.add_incidence(v1, v2);
         self.add_incidence(v2, v1);
+        Incidence(self.incidences.len() - 2)
     }
 }
 
diff --git a/src/traits.rs b/src/traits.rs
index 8a06dec..d4de040 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -1,5 +1,6 @@
 pub trait GraphTopology {
     type Vertex: Copy + Eq;
+    type Edge;
 
     fn vertex_count(&self) -> usize;
     fn edge_count(&self) -> usize;
@@ -8,5 +9,5 @@ pub trait GraphTopology {
     fn vertices(&self) -> impl Iterator<Item = Self::Vertex>;
     fn neighbors(&self, v: Self::Vertex) -> impl Iterator<Item = Self::Vertex>;
     fn add_vertex(&mut self) -> Self::Vertex;
-    fn add_edge(&mut self, v1: Self::Vertex, v2: Self::Vertex);
+    fn add_edge(&mut self, v1: Self::Vertex, v2: Self::Vertex) -> Self::Edge;
 }