diff --git a/src/algorithms/fill_bags_along_path.rs b/src/algorithms/fill_bags_along_path.rs
new file mode 100644
index 0000000..00c2392
--- /dev/null
+++ b/src/algorithms/fill_bags_along_path.rs
@@ -0,0 +1,97 @@
+use super::find_path_in_tree::find_path_in_tree;
+use itertools::Itertools;
+use petgraph::{
+    graph::NodeIndex,
+    visit::{IntoNodeReferences, NodeRef},
+    Graph,
+};
+use std::collections::HashSet;
+
+/// Given a tree graph with bags (HashSets) as Vertices, checks all 2-combinations of bags for non-empty-intersection
+/// and inserts the intersecting nodes in all bags that are along the (unique) path of the two bags in the tree.
+pub fn fill_bags_along_path<E>(
+    mut graph: Graph<HashSet<NodeIndex>, E, petgraph::prelude::Undirected>,
+) {
+    let mut vec_of_bags_that_need_to_be_connected: Vec<(NodeIndex, NodeIndex, Vec<NodeIndex>)> =
+        Vec::new();
+
+    // Finding out which paths between bags have to be checked
+    for mut vec in graph.node_references().combinations(2) {
+        let first_tuple = vec.pop().expect("Vec should contain two items");
+        let second_tuple = vec.pop().expect("Vec should contain two items");
+        let (first_id, first_weight, second_id, second_weight) = (
+            first_tuple.id(),
+            first_tuple.weight(),
+            second_tuple.id(),
+            second_tuple.weight(),
+        );
+
+        let mut intersection_iterator = first_weight.intersection(second_weight).cloned();
+        if let Some(vertex_in_both_bags) = intersection_iterator.next() {
+            let mut intersection_vec: Vec<NodeIndex> = intersection_iterator.collect();
+            intersection_vec.push(vertex_in_both_bags);
+            vec_of_bags_that_need_to_be_connected.push((first_id, second_id, intersection_vec));
+        }
+    }
+
+    // Filling up the bags along the paths of the vertices
+    for (first_id, second_id, intersection_vec) in vec_of_bags_that_need_to_be_connected {
+        let mut path = find_path_in_tree::<
+            &Graph<HashSet<NodeIndex>, E, petgraph::prelude::Undirected>,
+            Vec<_>,
+        >(&graph, first_id, second_id)
+        .expect("Paths should exist between all 2 vertices in a tree");
+
+        // Last element is the given end node
+        path.pop();
+
+        // Add the elements that are in both the bag of the starting and end vertex to all bags
+        // of the vertices on the path between them
+        for node_index in path {
+            if node_index != first_id {
+                graph
+                    .node_weight_mut(node_index)
+                    .expect("Bag for the vertex should exist")
+                    .extend(intersection_vec.iter().cloned());
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use petgraph::Graph;
+
+    use super::*;
+
+    #[test]
+    fn test() {
+        let mut graph: Graph<u32, u32, petgraph::prelude::Undirected> =
+            petgraph::Graph::new_undirected();
+
+        let nodes = [
+            graph.add_node(0),
+            graph.add_node(0),
+            graph.add_node(0),
+            graph.add_node(0),
+            graph.add_node(0),
+            graph.add_node(0),
+            graph.add_node(0),
+        ];
+
+        graph.add_edge(nodes[0], nodes[1], 0);
+        graph.add_edge(nodes[0], nodes[2], 0);
+        graph.add_edge(nodes[0], nodes[5], 0);
+        graph.add_edge(nodes[1], nodes[2], 0);
+        graph.add_edge(nodes[1], nodes[3], 0);
+        graph.add_edge(nodes[1], nodes[5], 0);
+        graph.add_edge(nodes[2], nodes[5], 0);
+        graph.add_edge(nodes[3], nodes[4], 0);
+        graph.add_edge(nodes[3], nodes[5], 0);
+        graph.add_edge(nodes[3], nodes[6], 0);
+        graph.add_edge(nodes[4], nodes[6], 0);
+
+        let min_spanning_tree_graph: Graph<u32, u32, petgraph::prelude::Undirected> =
+            petgraph::data::FromElements::from_elements(petgraph::algo::min_spanning_tree(&graph));
+    }
+}