diff --git a/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/shortestpath/Label.java b/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/shortestpath/Label.java
new file mode 100644
index 0000000..e69de29
diff --git a/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java b/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java
index a5073cd..c2aada8 100644
--- a/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java
+++ b/be-graphes-algos/src/main/java/org/insa/graphs/algorithm/utils/BinaryHeap.java
@@ -134,7 +134,16 @@ public class BinaryHeap<E extends Comparable<E>> implements PriorityQueue<E> {
 
     @Override
     public void remove(E x) throws ElementNotFoundException {
-        // TODO:
+        int index =this.array.indexOf(x);
+        if (index==-1||index>this.currentSize-1) {
+            throw new ElementNotFoundException(x);
+
+        }
+    E lastItem=this.array.get(--this.currentSize);
+    this.arraySet(index, lastItem);
+    this.percolateUp(index);
+    this.percolateDown(index);
+
     }
 
     @Override
diff --git a/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java b/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
index b9accf1..f4d345d 100644
--- a/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
+++ b/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
@@ -29,23 +29,31 @@ public class Path {
      */
     public static Path createFastestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
-        List<Arc> arcs = new ArrayList<Arc>();
-        if (nodes.size() <= 2){
-            throw new IllegalArgumentException(); 
-        }else{
-            for (int j = 0; j < nodes.size(); j++){
-                Node premier = nodes.get(j);
-                List<Arc> suc = premier.getSuccessors();
-                Arc elu = suc.get(0);
-                for (int i=0; i < suc.size(); i++){
+            if (nodes.isEmpty()){
+                return new Path(graph);
+            }
+        if (nodes.size()==1){
+            return new Path(graph,nodes.get(0));
+        }
+            List<Arc> arcs = new ArrayList<>();
+        for (int i=0;i<nodes.size()-1;i++){
+            Node noeud1=nodes.get(i);
+            Node suivant=nodes.get(i+1);
+            Arc choisi=null;
 
-                    if ( suc.get(i).getMinimumTravelTime() <= elu.getMinimumTravelTime()){
-                        elu = suc.get(i);
+            for (Arc arc :noeud1.getSuccessors()){
+                if (arc.getDestination().equals(suivant)){
+                    if(choisi==null|| arc.getMinimumTravelTime()<choisi.getMinimumTravelTime()){
+                        choisi=arc;
                     }
-                    arcs.add(elu);
                 }
             }
-        } 
+            if (choisi==null){
+                throw new IllegalArgumentException();
+            }
+            arcs.add(choisi);
+        }
+        
         return new Path(graph, arcs);
     }
 
@@ -62,24 +70,30 @@ public class Path {
      */
     public static Path createShortestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
-        List<Arc> arcs = new ArrayList<Arc>();
-        if (nodes.size() <= 2){
-            throw new IllegalArgumentException(); 
-        }else{
-            for (int j = 0; j < nodes.size(); j++){
-                Node premier = nodes.get(j);
-                List<Arc> suc = premier.getSuccessors();
-                Arc elu = suc.get(0);
-                for (int i=0; i < suc.size(); i++){
+         if (nodes.isEmpty()){
+                return new Path(graph);
+            }
+        if (nodes.size()==1){
+            return new Path(graph,nodes.get(0));
+        }
+            List<Arc> arcs = new ArrayList<>();
+        for (int i=0;i<nodes.size()-1;i++){
+            Node noeud1=nodes.get(i);
+            Node suivant=nodes.get(i+1);
+            Arc choisi=null;
 
-                    if ( suc.get(i).getLength() <= elu.getLength()){
-                        elu = suc.get(i);
+            for (Arc arc :noeud1.getSuccessors()){
+                if (arc.getDestination().equals(suivant)){
+                    if(choisi==null|| arc.getLength()<choisi.getLength()){
+                        choisi=arc;
                     }
-                    arcs.add(elu);
                 }
             }
+            if (choisi==null){
+                throw new IllegalArgumentException();
+            }
+            arcs.add(choisi);
         }
-        
 
         return new Path(graph, arcs);
     }
@@ -218,34 +232,27 @@ public class Path {
      * @return true if the path is valid, false otherwise.
      * @deprecated Need to be implemented.
      */
-     public boolean isValid() {
-        if(this.arcs.isEmpty()){
-            return true ; 
-        }
-        if ( this.graph.getNodes().size() <= 1 ){
-            return true ; 
-        }
-        
-        Node origin = this.graph.getNodes().getFirst(); // à revoir ( on prend deux arcs quelconque et compare )
-        List<Arc> firstSucs = origin.getSuccessors();
-        List<Node> destFirstArc = new ArrayList<>() ; 
-        for( Arc fSuc : firstSucs){
-            destFirstArc.add(fSuc.getDestination()) ;
-
-        } 
-        for (Node secondNode : destFirstArc){
-           List<Arc> secondSucs = secondNode.getSuccessors();
-            for (Arc sSuc : secondSucs){
-                if ( sSuc.getDestination() == origin){
-                    return true ; 
-                }
-            }
-        
-        }
-
-        return false;
-    
+ public boolean isValid() {
+    // Cas 1 : chemin vide
+    if (this.isEmpty()) {
+        return true;
     }
+    // Cas 2 : nœud unique, pas d'arcs
+    if (this.arcs.isEmpty()) {
+        return true;
+    }
+    // Cas 3 : le premier arc doit partir de l'origine
+    if (!this.arcs.get(0).getOrigin().equals(this.origin)) {
+        return false;
+    }
+    // Cas 4 : chaque arc doit enchaîner sur le suivant
+    for (int i = 0; i < this.arcs.size() - 1; i++) {
+        if (!this.arcs.get(i).getDestination().equals(this.arcs.get(i + 1).getOrigin())) {
+            return false;
+        }
+    }
+    return true;
+}
 
     /**
      * Compute the length of this path (in meters).
diff --git a/be-graphes-model/src/test/java/org/insa/graphes/model/PathTest.java b/be-graphes-model/src/test/java/org/insa/graphes/model/PathTest.java
index 8d10b74..0dbf42c 100644
--- a/be-graphes-model/src/test/java/org/insa/graphes/model/PathTest.java
+++ b/be-graphes-model/src/test/java/org/insa/graphes/model/PathTest.java
@@ -179,6 +179,7 @@ public class PathTest {
         for (int i = 0; i < expected.length; ++i) {
             assertEquals(expected[i], path.getArcs().get(i));
         }
+        
 
         // Not so simple construction
         path = Path.createFastestPathFromNodes(graph,