public void BuildGraph( 
   Geometry extent,
   Action<TopologyGraph> callBack
)

public void ExploreTopologyGraph()
{
  using (Geodatabase geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(new Uri(@"C:\TestData\GrandTeton.gdb"))))
  using (Topology topology = geodatabase.OpenDataset<Topology>("Backcountry_Topology"))
  {
    // Build a topology graph using the extent of the topology dataset.

    topology.BuildGraph(topology.GetExtent(), (topologyGraph) =>
    {
      using (Feature campsites12 = GetFeature(geodatabase, "Campsites", 12))
      {
        IReadOnlyList<TopologyNode> topologyNodesViaCampsites12 = topologyGraph.GetNodes(campsites12);

        TopologyNode topologyNodeViaCampsites12 = topologyNodesViaCampsites12[0];

        IReadOnlyList<TopologyEdge> allEdgesConnectedToNodeViaCampsites12 = topologyNodeViaCampsites12.GetEdges();
        IReadOnlyList<TopologyEdge> allEdgesConnectedToNodeViaCampsites12CounterClockwise = topologyNodeViaCampsites12.GetEdges(false);

        System.Diagnostics.Debug.Assert(allEdgesConnectedToNodeViaCampsites12.Count == allEdgesConnectedToNodeViaCampsites12CounterClockwise.Count);

        foreach (TopologyEdge edgeConnectedToNodeViaCampsites12 in allEdgesConnectedToNodeViaCampsites12)
        {
          TopologyNode fromNode = edgeConnectedToNodeViaCampsites12.GetFromNode();
          TopologyNode toNode = edgeConnectedToNodeViaCampsites12.GetToNode();

          bool fromNodeIsTheSameAsTopologyNodeViaCampsites12 = (fromNode == topologyNodeViaCampsites12);
          bool toNodeIsTheSameAsTopologyNodeViaCampsites12 = (toNode == topologyNodeViaCampsites12);

          System.Diagnostics.Debug.Assert(fromNodeIsTheSameAsTopologyNodeViaCampsites12 || toNodeIsTheSameAsTopologyNodeViaCampsites12,
            "The FromNode *or* ToNode of each edge connected to 'topologyNodeViaCampsites12' should be the same as 'topologyNodeViaCampsites12' itself.");

          IReadOnlyList<FeatureInfo> leftParentFeaturesBoundedByEdge = edgeConnectedToNodeViaCampsites12.GetLeftParentFeatures();
          foreach (FeatureInfo featureInfo in leftParentFeaturesBoundedByEdge)
          {
            System.Diagnostics.Debug.Assert(!String.IsNullOrEmpty(featureInfo.FeatureClassName));
            System.Diagnostics.Debug.Assert(featureInfo.ObjectID > 0);
            EnsureShapeIsNotEmpty(featureInfo);
          }

          IReadOnlyList<FeatureInfo> leftParentFeaturesNotBoundedByEdge = edgeConnectedToNodeViaCampsites12.GetLeftParentFeatures(false);
          foreach (FeatureInfo featureInfo in leftParentFeaturesNotBoundedByEdge)
          {
            System.Diagnostics.Debug.Assert(!String.IsNullOrEmpty(featureInfo.FeatureClassName));
            System.Diagnostics.Debug.Assert(featureInfo.ObjectID > 0);
            EnsureShapeIsNotEmpty(featureInfo);
          }

          IReadOnlyList<FeatureInfo> rightParentFeaturesBoundedByEdge = edgeConnectedToNodeViaCampsites12.GetRightParentFeatures();
          foreach (FeatureInfo featureInfo in rightParentFeaturesBoundedByEdge)
          {
            System.Diagnostics.Debug.Assert(!String.IsNullOrEmpty(featureInfo.FeatureClassName));
            System.Diagnostics.Debug.Assert(featureInfo.ObjectID > 0);
            EnsureShapeIsNotEmpty(featureInfo);
          }

          IReadOnlyList<FeatureInfo> rightParentFeaturesNotBoundedByEdge = edgeConnectedToNodeViaCampsites12.GetRightParentFeatures(false);
          foreach (FeatureInfo featureInfo in rightParentFeaturesNotBoundedByEdge)
          {
            System.Diagnostics.Debug.Assert(!String.IsNullOrEmpty(featureInfo.FeatureClassName));
            System.Diagnostics.Debug.Assert(featureInfo.ObjectID > 0);
            EnsureShapeIsNotEmpty(featureInfo);
          }
        }
      }
    });
  }
}

private void EnsureShapeIsNotEmpty(FeatureInfo featureInfo)
{
  using (Feature feature = featureInfo.GetFeature())
  {
    System.Diagnostics.Debug.Assert(!feature.GetShape().IsEmpty, "The feature's shape should not be empty.");
  }
}