diff --git a/api/server/src/main/java/org/softwareheritage/graph/App.java b/api/server/src/main/java/org/softwareheritage/graph/App.java
--- a/api/server/src/main/java/org/softwareheritage/graph/App.java
+++ b/api/server/src/main/java/org/softwareheritage/graph/App.java
@@ -56,7 +56,7 @@
         // By default, traversal is a forward DFS using all edges
         String traversal = ctx.queryParam("traversal", "dfs");
         String direction = ctx.queryParam("direction", "forward");
-        String edges = ctx.queryParam("edges", "all");
+        String edges = ctx.queryParam("edges", "*");
 
         ctx.json(new Visit(graph, swhId, edges, traversal, direction));
       } catch (IllegalArgumentException e) {
diff --git a/api/server/src/main/java/org/softwareheritage/graph/Edges.java b/api/server/src/main/java/org/softwareheritage/graph/Edges.java
new file mode 100644
--- /dev/null
+++ b/api/server/src/main/java/org/softwareheritage/graph/Edges.java
@@ -0,0 +1,47 @@
+package org.softwareheritage.graph;
+
+import java.util.ArrayList;
+
+import org.softwareheritage.graph.Node;
+
+public class Edges {
+  boolean[][] allowed;
+
+  public Edges(String edgesFmt) {
+    int nbNodeTypes = Node.Type.values().length;
+    this.allowed = new boolean[nbNodeTypes][nbNodeTypes];
+    // Special values (null, empty, "*")
+    if (edgesFmt == null || edgesFmt.isEmpty()) {
+      return;
+    }
+    if (edgesFmt.equals("*")) {
+      for (int i = 0; i < nbNodeTypes; i++) {
+        for (int j = 0; j < nbNodeTypes; j++) {
+          allowed[i][j] = true;
+        }
+      }
+      return;
+    }
+
+    // Format: "src1:dst1,src2:dst2,[...]"
+    String[] edgeTypes = edgesFmt.split(",");
+    for (String edgeType : edgeTypes) {
+      String[] nodeTypes = edgeType.split(":");
+      if (nodeTypes.length != 2) {
+        throw new IllegalArgumentException("Cannot parse edge type: " + edgeType);
+      }
+
+      ArrayList<Node.Type> srcTypes = Node.Type.parse(nodeTypes[0]);
+      ArrayList<Node.Type> dstTypes = Node.Type.parse(nodeTypes[1]);
+      for (Node.Type srcType : srcTypes) {
+        for (Node.Type dstType : dstTypes) {
+          allowed[srcType.ordinal()][dstType.ordinal()] = true;
+        }
+      }
+    }
+  }
+
+  public boolean isAllowed(Node.Type currentType, Node.Type neighborType) {
+    return allowed[currentType.ordinal()][neighborType.ordinal()];
+  }
+}
diff --git a/api/server/src/main/java/org/softwareheritage/graph/Node.java b/api/server/src/main/java/org/softwareheritage/graph/Node.java
new file mode 100644
--- /dev/null
+++ b/api/server/src/main/java/org/softwareheritage/graph/Node.java
@@ -0,0 +1,32 @@
+package org.softwareheritage.graph;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+public class Node {
+  public enum Type {
+    CNT,
+    DIR,
+    REL,
+    REV,
+    SNP;
+
+    public static Node.Type fromStr(String strType) {
+      return Node.Type.valueOf(strType.toUpperCase());
+    }
+
+    public static ArrayList<Node.Type> parse(String strType) {
+      ArrayList<Node.Type> types = new ArrayList<>();
+
+      if (strType.equals("*")) {
+        List<Node.Type> nodeTypes = Arrays.asList(Node.Type.values());
+        types.addAll(nodeTypes);
+      } else {
+        types.add(Node.Type.fromStr(strType));
+      }
+
+      return types;
+    }
+  }
+}
diff --git a/api/server/src/main/java/org/softwareheritage/graph/SwhId.java b/api/server/src/main/java/org/softwareheritage/graph/SwhId.java
--- a/api/server/src/main/java/org/softwareheritage/graph/SwhId.java
+++ b/api/server/src/main/java/org/softwareheritage/graph/SwhId.java
@@ -2,11 +2,13 @@
 
 import com.fasterxml.jackson.annotation.JsonValue;
 
+import org.softwareheritage.graph.Node;
+
 public class SwhId {
   public static final int HASH_LENGTH = 40;
 
   String swhId;
-  String type;
+  Node.Type type;
   String hash;
 
   // SWH ID format: 'swh:1:type:hash'
@@ -19,10 +21,11 @@
       throw new IllegalArgumentException("Expected SWH ID format to be 'swh:1:type:hash', got: " + swhId);
     }
 
-    this.type = parts[2];
+    String type = parts[2];
     if (!type.matches("cnt|dir|rel|rev|snp")) {
       throw new IllegalArgumentException("Unknown SWH ID type in: " + swhId);
     }
+    this.type = Node.Type.fromStr(type);
 
     this.hash = parts[3];
     if (!hash.matches("[0-9a-f]{" + HASH_LENGTH + "}")) {
@@ -49,7 +52,7 @@
     return swhId;
   }
 
-  public String getType() {
+  public Node.Type getType() {
     return type;
   }
 
diff --git a/api/server/src/main/java/org/softwareheritage/graph/algo/Visit.java b/api/server/src/main/java/org/softwareheritage/graph/algo/Visit.java
--- a/api/server/src/main/java/org/softwareheritage/graph/algo/Visit.java
+++ b/api/server/src/main/java/org/softwareheritage/graph/algo/Visit.java
@@ -5,14 +5,16 @@
 
 import it.unimi.dsi.big.webgraph.LazyLongIterator;
 
+import org.softwareheritage.graph.Edges;
 import org.softwareheritage.graph.Graph;
+import org.softwareheritage.graph.Node;
 import org.softwareheritage.graph.SwhId;
 import org.softwareheritage.graph.SwhPath;
 
 public class Visit {
   Graph graph;
   boolean useTransposed;
-  String allowedEdges;
+  Edges edges;
   Stack<Long> currentPath;
   ArrayList<SwhPath> paths;
 
@@ -26,7 +28,7 @@
 
     this.graph = graph;
     this.useTransposed = (direction.equals("backward"));
-    this.allowedEdges = allowedEdges;
+    this.edges = new Edges(allowedEdges);
     this.paths = new ArrayList<SwhPath>();
     this.currentPath = new Stack<Long>();
 
@@ -49,7 +51,9 @@
 
     while (degree-- > 0) {
       long neighborNodeId = neighbors.nextLong();
-      if (isEdgeAllowed(currentNodeId, neighborNodeId)) {
+      Node.Type currentNodeType = graph.getSwhId(currentNodeId).getType();
+      Node.Type neighborNodeType = graph.getSwhId(neighborNodeId).getType();
+      if (edges.isAllowed(currentNodeType, neighborNodeType)) {
         dfs(neighborNodeId);
         visitedNeighbors++;
       }
@@ -65,16 +69,4 @@
 
     currentPath.pop();
   }
-
-  private boolean isEdgeAllowed(long currentNodeId, long neighborNodeId) {
-    if (allowedEdges.equals("all")) {
-      return true;
-    }
-
-    String currentType = graph.getSwhId(currentNodeId).getType();
-    String neighborType = graph.getSwhId(neighborNodeId).getType();
-    String edgeType = currentType + ":" + neighborType;
-    String edgeTypeRev = neighborType + ":" + currentType;
-    return allowedEdges.contains(edgeType) || allowedEdges.contains(edgeTypeRev);
-  }
 }