public string FeatureClassName {get;}

{
  static void ExploreTopologyGraph()
  {
    using (Geodatabase geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(new Uri(@"C:\TestData\GrandTeton.gdb"))))
    using (ArcGIS.Core.Data.Topology.Topology topology = geodatabase.OpenDataset<ArcGIS.Core.Data.Topology.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);

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

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

            IReadOnlyList<FeatureInfo> leftParentFeaturesBoundedByEdge =
              edgeConnectedToNodeViaCampsites12.GetLeftParentFeatures();
            foreach (FeatureInfo featureInfo in leftParentFeaturesBoundedByEdge)
            {
              EnsureShapeIsNotEmpty(featureInfo);
            }

            IReadOnlyList<FeatureInfo> leftParentFeaturesNotBoundedByEdge =
              edgeConnectedToNodeViaCampsites12.GetLeftParentFeatures(false);
            foreach (FeatureInfo featureInfo in leftParentFeaturesNotBoundedByEdge)
            {
              EnsureShapeIsNotEmpty(featureInfo);
            }

            IReadOnlyList<FeatureInfo> rightParentFeaturesBoundedByEdge =
              edgeConnectedToNodeViaCampsites12.GetRightParentFeatures();
            foreach (FeatureInfo featureInfo in rightParentFeaturesBoundedByEdge)
            {
              EnsureShapeIsNotEmpty(featureInfo);
            }

            IReadOnlyList<FeatureInfo> rightParentFeaturesNotBoundedByEdge =
              edgeConnectedToNodeViaCampsites12.GetRightParentFeatures(false);
            foreach (FeatureInfo featureInfo in rightParentFeaturesNotBoundedByEdge)
            {
              EnsureShapeIsNotEmpty(featureInfo);
            }
          }
        }
      });
    }
    static void EnsureShapeIsNotEmpty(FeatureInfo featureInfo)
    {
      using (Feature feature = featureInfo.GetFeature())
      {
        // Process feature ...
      }
    }
  }
}

{
  static void FindClosestElement()
  {
    using (Geodatabase geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(new Uri(@"C:\TestData\GrandTeton.gdb"))))
    using (ArcGIS.Core.Data.Topology.Topology topology = geodatabase.OpenDataset<ArcGIS.Core.Data.Topology.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);
        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.
        }
      });
    }
  }
}