public Envelope GetExtent()

public void ValidateTopology()
{
  using (Geodatabase geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(new Uri(@"C:\TestData\GrandTeton.gdb"))))
  using (Topology topology = geodatabase.OpenDataset<Topology>("Backcountry_Topology"))
  {
    // If the topology currently does not have dirty areas, calling Validate() returns an empty envelope.

    ValidationResult result = topology.Validate(new ValidationDescription(topology.GetExtent()));
    Console.WriteLine($"'AffectedArea' after validating a topology that has not been edited => {result.AffectedArea.ToJson()}");

    // Now create a feature that purposely violates the "PointProperlyInsideArea" topology rule.  This action will
    // create dirty areas.

    Feature newFeature = null;

    try
    {
      // Fetch the feature in the Campsites feature class whose objectID is 2.  Then create a new geometry slightly
      // altered from this and use it to create a new feature.

      using (Feature featureViaCampsites2 = GetFeature(geodatabase, "Campsites", 2))
      {
        Geometry currentGeometry = featureViaCampsites2.GetShape();
        Geometry newGeometry = GeometryEngine.Instance.Move(currentGeometry, (currentGeometry.Extent.XMax / 8),
          (currentGeometry.Extent.YMax / 8));

        using (FeatureClass campsitesFeatureClass = featureViaCampsites2.GetTable())
        using (FeatureClassDefinition definition = campsitesFeatureClass.GetDefinition())
        using (RowBuffer rowBuffer = campsitesFeatureClass.CreateRowBuffer())
        {
          rowBuffer[definition.GetShapeField()] = newGeometry;

          geodatabase.ApplyEdits(() =>
          {
            newFeature = campsitesFeatureClass.CreateRow(rowBuffer);
          });
        }
      }

      // After creating a new feature in the 'Campsites' participating feature class, the topology's state should be 
      // "Unanalyzed" because it has not been validated.

      Console.WriteLine($"The topology state after an edit has been applied => {topology.GetState()}");

      // Now validate the topology.  The result envelope corresponds to the dirty areas.

      result = topology.Validate(new ValidationDescription(topology.GetExtent()));
      Console.WriteLine($"'AffectedArea' after validating a topology that has just been edited => {result.AffectedArea.ToJson()}");

      // After Validate(), the topology's state should be "AnalyzedWithErrors" because the topology currently has errors.

      Console.WriteLine($"The topology state after validate topology => {topology.GetState()}");

      // If there are no dirty areas, the result envelope should be empty.

      result = topology.Validate(new ValidationDescription(topology.GetExtent()));
      Console.WriteLine($"'AffectedArea' after validating a topology that has just been validated => {result.AffectedArea.ToJson()}");
    }
    finally
    {
      if (newFeature != null)
      {
        geodatabase.ApplyEdits(() =>
        {
          newFeature.Delete();
        });

        newFeature.Dispose();
      }
    }

    // Validate again after deleting the newly-created feature.

    topology.Validate(new ValidationDescription(topology.GetExtent()));
  }
}

private Feature GetFeature(Geodatabase geodatabase, string featureClassName, long objectID)
{
  using (FeatureClass featureClass = geodatabase.OpenDataset<FeatureClass>(featureClassName))
  {
    QueryFilter queryFilter = new QueryFilter()
    {
      ObjectIDs = new List<long>() { objectID }
    };

    using (RowCursor cursor = featureClass.Search(queryFilter))
    {
      System.Diagnostics.Debug.Assert(cursor.MoveNext());
      return (Feature)cursor.Current;
    }
  }
}

// Get all the errors due to features violating the "PointProperlyInsideArea" topology rule.

using (TopologyDefinition topologyDefinition = topology.GetDefinition())
{
  TopologyRule pointProperlyInsideAreaRule = topologyDefinition.GetRules().First(rule => rule.RuleType == TopologyRuleType.PointProperlyInsideArea);

  ErrorDescription errorDescription = new ErrorDescription(topology.GetExtent())
  {
    TopologyRule = pointProperlyInsideAreaRule
  };

  IReadOnlyList<TopologyError> errorsDueToViolatingPointProperlyInsideAreaRule = topology.GetErrors(errorDescription);
  Console.WriteLine($"There are {errorsDueToViolatingPointProperlyInsideAreaRule.Count} feature violating the 'PointProperlyInsideArea' topology rule.");

  // Mark all errors from features violating the 'PointProperlyInsideArea' topology rule as exceptions.

  foreach (TopologyError error in errorsDueToViolatingPointProperlyInsideAreaRule)
  {
    topology.MarkAsException(error);
  }

  // Now verify all the errors from features violating the 'PointProperlyInsideArea' topology rule have indeed been
  // marked as exceptions.
  //
  // By default, ErrorDescription is initialized to ErrorType.ErrorAndException.  Here we want ErrorType.ErrorOnly.

  errorDescription = new ErrorDescription(topology.GetExtent())
  {
    ErrorType = ErrorType.ErrorOnly,
    TopologyRule = pointProperlyInsideAreaRule
  };

  IReadOnlyList<TopologyError> errorsAfterMarkedAsExceptions = topology.GetErrors(errorDescription);
  Console.WriteLine($"There are {errorsAfterMarkedAsExceptions.Count} feature violating the 'PointProperlyInsideArea' topology rule after all the errors have been marked as exceptions.");

  // Finally, reset all the exceptions as errors by unmarking them as exceptions.

  foreach (TopologyError error in errorsDueToViolatingPointProperlyInsideAreaRule)
  {
    topology.UnmarkAsException(error);
  }

  IReadOnlyList<TopologyError> errorsAfterUnmarkedAsExceptions = topology.GetErrors(errorDescription);
  Console.WriteLine($"There are {errorsAfterUnmarkedAsExceptions.Count} feature violating the 'PointProperlyInsideArea' topology rule after all the exceptions have been reset as errors.");
}

public void FindClosestElement()
{
  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) =>
    {
      MapPoint queryPointViaCampsites12 = null;

      using (Feature campsites12 = GetFeature(geodatabase, "Campsites", 12))
      {
        queryPointViaCampsites12 = campsites12.GetShape() as MapPoint;
      }

      double searchRadius = 1.0;

      TopologyElement topologyElementViaCampsites12 = 
          topologyGraph.FindClosestElement<TopologyElement>(
                    queryPointViaCampsites12, searchRadius);

      System.Diagnostics.Debug.Assert(
        topologyElementViaCampsites12 != null, "There should be a topology element corresponding to 'queryPointViaCampsites12' within the 'searchRadius' units.");

      IReadOnlyList<FeatureInfo> parentFeatures = topologyElementViaCampsites12.GetParentFeatures();

      Console.WriteLine("The parent features that spawn 'topologyElementViaCampsites12' are:");
      foreach (FeatureInfo parentFeature in parentFeatures)
      {
        Console.WriteLine($"\t{parentFeature.FeatureClassName}; OID: {parentFeature.ObjectID}");
      }

      TopologyNode topologyNodeViaCampsites12 = topologyGraph.FindClosestElement<TopologyNode>(queryPointViaCampsites12, searchRadius);

      if (topologyNodeViaCampsites12 != null)
      {
        // There exists a TopologyNode nearest to the query point within searchRadius units.
      }

      TopologyEdge topologyEdgeViaCampsites12 = topologyGraph.FindClosestElement<TopologyEdge>(queryPointViaCampsites12, searchRadius);

      if (topologyEdgeViaCampsites12 != null)
      {
        // There exists a TopologyEdge nearest to the query point within searchRadius units.
      }
    });
  }
}