diff --git a/Cargo.lock b/Cargo.lock
index 66690bc6..aea4b656 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -120,6 +120,12 @@ version = "1.0.98"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e16d2d3311acee920a9eb8d33b8cbc1787ce4a264e85f964c2404b969bdcd487"
 
+[[package]]
+name = "aph_disjoint_set"
+version = "0.1.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ec916e7c5883e65b44aead1b3b77c144e518686472524896868cb00366937c08"
+
 [[package]]
 name = "approx"
 version = "0.5.1"
@@ -1438,6 +1444,7 @@ dependencies = [
 name = "layir"
 version = "0.2.1"
 dependencies = [
+ "aph_disjoint_set",
  "arcstr",
  "enumify",
  "geometry",
diff --git a/docs/docusaurus/yarn.lock b/docs/docusaurus/yarn.lock
index f05b3cab..b559f25d 100644
--- a/docs/docusaurus/yarn.lock
+++ b/docs/docusaurus/yarn.lock
@@ -8522,9 +8522,9 @@ typedarray-to-buffer@^3.1.5:
     is-typedarray "^1.0.0"
 
 typescript@~5.8.0:
-  version "5.8.2"
-  resolved "https://registry.yarnpkg.com/typescript/-/typescript-5.8.2.tgz#8170b3702f74b79db2e5a96207c15e65807999e4"
-  integrity sha512-aJn6wq13/afZp/jT9QZmwEjDqqvSGp1VT5GVg+f/t6/oVyrgXM6BY1h9BRh/O5p3PlUPAe+WuiEZOmb/49RqoQ==
+  version "5.8.3"
+  resolved "https://registry.yarnpkg.com/typescript/-/typescript-5.8.3.tgz#92f8a3e5e3cf497356f4178c34cd65a7f5e8440e"
+  integrity sha512-p1diW6TqL9L07nNxvRMM7hMMw4c5XOo/1ibL4aAIGmSAt9slTE1Xgw5KWuof2uTOvCg9BY7ZRi+GaF+7sfgPeQ==
 
 undici-types@~6.20.0:
   version "6.20.0"
diff --git a/libs/layir/Cargo.toml b/libs/layir/Cargo.toml
index 7297afb9..764b1ad3 100644
--- a/libs/layir/Cargo.toml
+++ b/libs/layir/Cargo.toml
@@ -13,4 +13,5 @@ thiserror = "2"
 enumify = { version = "0.2.1", registry = "substrate", path = "../enumify" }
 uniquify = { version = "0.4.0", registry = "substrate", path = "../uniquify" }
 geometry = { version = "0.7.1", registry = "substrate", path = "../geometry" }
+aph_disjoint_set = "0.1.0"
 
diff --git a/libs/layir/src/connectivity.rs b/libs/layir/src/connectivity.rs
new file mode 100644
index 00000000..5a0191a1
--- /dev/null
+++ b/libs/layir/src/connectivity.rs
@@ -0,0 +1,244 @@
+use crate::CellId;
+use crate::Instance;
+use aph_disjoint_set::DisjointSet;
+use geometry::bbox::Bbox;
+use geometry::rect::Rect;
+use std::collections::{HashMap, HashSet};
+use std::hash::Hash;
+
+use crate::Element;
+use crate::{Cell, Library, Shape, TransformRef, Transformation};
+
+/// Returns true if two shapes overlap on a flat plane, and false otherwise.
+fn intersect_shapes<L>(shape1: &Shape<L>, shape2: &Shape<L>) -> bool {
+    let shape1_bbox: Rect = shape1.bbox_rect();
+    let shape2_bbox: Rect = shape2.bbox_rect();
+    shape1_bbox.intersection(shape2_bbox).is_some()
+}
+
+/// Returns a vector of all shapes from a given cell instance and its children
+/// with their coordinates transformed into the coordinate system of the instance's parent.
+fn flatten_instance<L>(inst: &Instance, lib: &Library<L>) -> Vec<Shape<L>>
+where
+    L: Connectivity + Clone,
+{
+    let mut ret: Vec<Shape<L>> = vec![];
+
+    let cellid: CellId = inst.child();
+    let transform: Transformation = inst.transformation();
+
+    // Add all shape elements directly from child cell after applying the instances transformation
+    for elem in lib.cell(cellid).elements() {
+        if let Element::Shape(shape) = elem {
+            let transformed_shape = shape.transform_ref(transform);
+            ret.push(transformed_shape);
+        }
+    }
+
+    // Recursively flatten child instances and apply cumulative transformations
+    for instance in lib.cell(cellid).instances() {
+        let mut flattened_shapes = flatten_instance::<L>(instance.1, lib);
+        for flattened_shape in &mut flattened_shapes {
+            *flattened_shape = flattened_shape.transform_ref(transform);
+        }
+        ret.append(&mut flattened_shapes);
+    }
+
+    ret
+}
+
+/// Returns a vector of all shapes from a single cell's transformed child instances and itself.
+fn flatten_cell<L>(cell: &Cell<L>, lib: &Library<L>) -> Vec<Shape<L>>
+where
+    L: Connectivity + Clone,
+{
+    let mut ret: Vec<Shape<L>> = vec![];
+
+    // No transformation needed
+    for elem in cell.elements() {
+        if let Element::Shape(shape) = elem {
+            ret.push(shape.clone());
+        }
+    }
+
+    for inst in cell.instances() {
+        for flattened_shape in flatten_instance::<L>(inst.1, lib) {
+            ret.push(flattened_shape);
+        }
+    }
+
+    ret
+}
+
+pub trait Connectivity: Sized + PartialEq + Eq + Clone + Hash {
+    fn connected_layers(&self) -> Vec<Self>;
+
+    /// Returns a vector of layers connected to a given layer.
+    fn connected(&self, other: &Self) -> bool {
+        self.connected_layers().contains(other)
+    }
+
+    /// Returns a vector of unique hashsets of all connected groups of connected child shapes in a given cell.
+    fn connected_components(cell: &Cell<Self>, lib: &Library<Self>) -> Vec<HashSet<Shape<Self>>>
+    where
+        Self: Clone,
+    {
+        // All sub-shapes contained in given cell
+        let all_shapes = flatten_cell::<Self>(cell, lib);
+        let mut djs = DisjointSet::new(all_shapes.len());
+
+        // Build disjoint sets based on overlap and layer connectivity
+        for (start_index, start_shape) in all_shapes.clone().into_iter().enumerate() {
+            for (other_index, other_shape) in all_shapes.clone().into_iter().enumerate() {
+                if start_index != other_index
+                    && intersect_shapes::<Self>(&start_shape, &other_shape)
+                    && start_shape.layer().connected(other_shape.layer())
+                {
+                    djs.union(start_index, other_index);
+                }
+            }
+        }
+
+        let mut component_map: HashMap<usize, HashSet<Shape<Self>>> = HashMap::new();
+
+        for (start_index, start_shape) in all_shapes.into_iter().enumerate() {
+            let root: usize = djs.get_root(start_index).into_inner();
+            component_map.entry(root).or_default().insert(start_shape);
+        }
+
+        component_map.into_values().collect()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{Cell, Instance, LibraryBuilder, Shape};
+    use geometry::rect::Rect;
+    use std::collections::{HashMap, HashSet};
+
+    // This struct helps check if two shapes are connected after connected_components has been run
+    struct ComponentLookup<L> {
+        shape_to_component_id: HashMap<Shape<L>, usize>,
+    }
+
+    impl<L> ComponentLookup<L>
+    where
+        L: Connectivity + Clone,
+    {
+        /// Creates a new ComponentLookup from a vector of connected components.
+        fn new(components: Vec<HashSet<Shape<L>>>) -> Self {
+            let mut shape_to_component_id = HashMap::new();
+            for (component_id, component_set) in components.into_iter().enumerate() {
+                for shape in component_set.into_iter() {
+                    shape_to_component_id.insert(shape, component_id);
+                }
+            }
+            ComponentLookup {
+                shape_to_component_id,
+            }
+        }
+
+        /// Returns true if both shapes are found and belong to the same component, and false otherwise.
+        fn are_connected(&self, s1: &Shape<L>, s2: &Shape<L>) -> bool {
+            let comp_id1 = self.shape_to_component_id.get(s1);
+            let comp_id2 = self.shape_to_component_id.get(s2);
+
+            match (comp_id1, comp_id2) {
+                // If both shapes are found, check if their component IDs are the same
+                (Some(&id1), Some(&id2)) => id1 == id2,
+                _ => false,
+            }
+        }
+    }
+
+    #[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
+    enum Layer {
+        Met1,
+        Via1,
+        Met2,
+        Outside,
+    }
+
+    impl Connectivity for Layer {
+        fn connected_layers(&self) -> Vec<Self> {
+            match self {
+                Self::Met1 => vec![Self::Met1, Self::Via1],
+                Self::Via1 => vec![Self::Met1, Self::Via1, Self::Met2],
+                Self::Met2 => vec![Self::Via1, Self::Met2],
+                Self::Outside => vec![],
+            }
+        }
+    }
+
+    #[test]
+    fn test_complete() {
+        let mut small_cell: Cell<Layer> = Cell::new("small cell test");
+        let mut big_cell: Cell<Layer> = Cell::new("big cell test");
+        let mut lib_builder: LibraryBuilder<Layer> = LibraryBuilder::new();
+
+        // Build small cell first and add to big cell
+        let m2_shape1 = Shape::new(Layer::Met2, Rect::from_sides(0, 0, 30, 30));
+        small_cell.add_element(m2_shape1.clone());
+
+        lib_builder.add_cell(small_cell.clone());
+        let small_cell_id = lib_builder.cells().next().unwrap().0;
+
+        let small_cell_instance = Instance::new(small_cell_id, "small_cell_test");
+        big_cell.add_instance(small_cell_instance);
+
+        // Build big cell
+        let m1_shape = Shape::new(Layer::Met1, Rect::from_sides(0, 0, 100, 100));
+        let v1_shape = Shape::new(Layer::Via1, Rect::from_sides(10, 10, 100, 100));
+        let m2_shape2 = Shape::new(Layer::Met2, Rect::from_sides(10, 10, 50, 50));
+        let m2_shape3 = Shape::new(Layer::Met2, Rect::from_sides(1000, 1000, 5000, 5000));
+        big_cell.add_element(m1_shape.clone());
+        big_cell.add_element(v1_shape.clone());
+        big_cell.add_element(m2_shape2.clone());
+        big_cell.add_element(m2_shape3.clone());
+
+        lib_builder.add_cell(big_cell.clone());
+
+        // Build fixed library
+        let lib = lib_builder.clone().build().unwrap();
+
+        // Add an outside shape for testing
+        let outside_shape = Shape::new(Layer::Outside, Rect::from_sides(0, 0, 100, 100));
+
+        // Find all connected components of big_cell's child shapes
+        let components_vec = Layer::connected_components(&big_cell, &lib);
+
+        let component_lookup = ComponentLookup::new(components_vec.clone());
+
+        // Expected connections
+        assert!(
+            component_lookup.are_connected(&m1_shape, &v1_shape),
+            "m1_shape should be connected to v1_shape"
+        );
+        assert!(
+            component_lookup.are_connected(&m1_shape, &m2_shape2),
+            "m1_shape should be connected to m2_shape2"
+        );
+        assert!(
+            component_lookup.are_connected(&m1_shape, &m2_shape1), // m2_shape1 is from the instance
+            "m1_shape should be connected to m2_shape1"
+        );
+
+        // Expected disconnection
+        assert!(
+            !component_lookup.are_connected(&m1_shape, &m2_shape3),
+            "m1_shape should not be connected to m2_shape3 (isolated)"
+        );
+        assert!(
+            !component_lookup.are_connected(&m1_shape, &outside_shape),
+            "m1_shape should not be connected to outside_shape"
+        );
+
+        // Double check number of connected components in library
+        assert_eq!(
+            components_vec.len(),
+            2,
+            "Expected 2 total connected components."
+        );
+    }
+}
diff --git a/libs/layir/src/lib.rs b/libs/layir/src/lib.rs
index 67831a0f..b2216a5d 100644
--- a/libs/layir/src/lib.rs
+++ b/libs/layir/src/lib.rs
@@ -1,5 +1,6 @@
 #![allow(dead_code)]
 
+pub mod connectivity;
 pub mod id;
 
 use std::{