diff --git a/Trajectories/Tests/example_2.graphml b/Trajectories/Tests/example_2.graphml
new file mode 100644
index 0000000000000000000000000000000000000000..45d4383851707a64c1c20556d3634e7a29b373bc
--- /dev/null
+++ b/Trajectories/Tests/example_2.graphml
@@ -0,0 +1,85 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<graphml xmlns="http://graphml.graphdrawing.org/xmlns"
+         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+         xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd">
+
+  <!-- property keys -->
+  <key id="key0" for="graph" attr.name="e_overestim" attr.type="int" />
+  <key id="key1" for="edge" attr.name="cost_function" attr.type="float" />
+  <key id="key2" for="node" attr.name="name" attr.type="string" />
+  <key id="key3" for="node" attr.name="inst_eddies" attr.type="vector_int" />
+
+  <graph id="G" edgedefault="directed" parse.nodeids="canonical" parse.edgeids="canonical" parse.order="nodesfirst">
+
+   <!-- graph properties -->
+   <data key="key0">10</data>
+
+   <!-- vertices -->
+    <node id="n0">
+      <data key="key2">1</data>
+      <data key="key3">1</data>
+    </node>
+    <node id="n1">
+      <data key="key2">11</data>
+      <data key="key3">11</data>
+    </node>
+    <node id="n2">
+      <data key="key2">12</data>
+      <data key="key3">12</data>
+    </node>
+    <node id="n3">
+      <data key="key2">21</data>
+      <data key="key3">21</data>
+    </node>
+    <node id="n4">
+      <data key="key2">22</data>
+      <data key="key3">22</data>
+    </node>
+    <node id="n5">
+      <data key="key2">31</data>
+      <data key="key3">31</data>
+    </node>
+    <node id="n6">
+      <data key="key2">41</data>
+      <data key="key3">41</data>
+    </node>
+    <node id="n7">
+      <data key="key2">42</data>
+      <data key="key3">42</data>
+    </node>
+    <node id="n8">
+      <data key="key2">51</data>
+      <data key="key3">51</data>
+    </node>
+
+   <!-- edges -->
+    <edge id="e0" source="n0" target="n1">
+      <data key="key1">0.5</data>
+    </edge>
+    <edge id="e1" source="n0" target="n2">
+      <data key="key1">5</data>
+    </edge>
+    <edge id="e2" source="n1" target="n5">
+      <data key="key1">3</data>
+    </edge>
+    <edge id="e3" source="n1" target="n3">
+      <data key="key1">4</data>
+    </edge>
+    <edge id="e4" source="n3" target="n6">
+      <data key="key1">1</data>
+    </edge>
+    <edge id="e5" source="n3" target="n7">
+      <data key="key1">0.5</data>
+    </edge>
+    <edge id="e6" source="n4" target="n7">
+      <data key="key1">0.1</data>
+    </edge>
+    <edge id="e7" source="n5" target="n8">
+      <data key="key1">4</data>
+    </edge>
+    <edge id="e8" source="n6" target="n8">
+      <data key="key1">0.5</data>
+    </edge>
+
+  </graph>
+</graphml>
diff --git a/Trajectories/Tests/tests.json b/Trajectories/Tests/tests.json
index 3c798c144725f76b4205852fb82acd8fa28f4780..388f70358fc47d9c2adb5fc810ec064f30940aac 100644
--- a/Trajectories/Tests/tests.json
+++ b/Trajectories/Tests/tests.json
@@ -133,5 +133,15 @@
 	],
 	"description": "A toy case of division followed by fusion.",
 	"input": "10"
+    },
+    "Test_order_edges":
+    {
+	"command":
+	[
+	    "$src_dir/Trajectories/trajectories.py",
+	    "$src_dir/Trajectories/Tests/example_2.graphml"
+	],
+	"description": "A toy case to test the algorithm in trajectories.py, specifically to test the order in which edges are processed.",
+	"input": "10"
     }
 }