public sealed class TopologyDefinition : ArcGIS.Core.Data.Definition, System.IDisposable  

// Builds the map topology graph for the active map view and displays the number of topology nodes and edges.
await QueuedTask.Run(() =>
{
  //Build the map topology graph
  MapView.Active.BuildMapTopologyGraph<TopologyDefinition>(topologyGraph =>
  {
    //Getting the nodes and edges present in the graph
    var topologyGraphNodes = topologyGraph.GetNodes();
    var topologyGraphEdges = topologyGraph.GetEdges();

    foreach (var node in topologyGraphNodes)
    {
      // do something with the node
    }
    foreach (var edge in topologyGraphEdges)
    {
      // do something with the edge
    }
    MessageBox.Show($"Number of topo graph nodes are:  {topologyGraphNodes.Count}.\n Number of topo graph edges are {topologyGraphEdges.Count}.", "Map Topology Info");
  });
});

{
  static void OpenTopologyAndProcessDefinition()
  {
    // Open a geodatabase topology from a file geodatabase and process the topology definition.
    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"))
    {
      ProcessDefinition(geodatabase, topology);
    }

    // Open a feature service topology and process the topology definition.
    const string TOPOLOGY_LAYER_ID = "0";

    using (Geodatabase geodatabase = new Geodatabase(new ServiceConnectionProperties(new Uri("https://sdkexamples.esri.com/server/rest/services/GrandTeton/FeatureServer"))))
    using (ArcGIS.Core.Data.Topology.Topology topology = geodatabase.OpenDataset<ArcGIS.Core.Data.Topology.Topology>(TOPOLOGY_LAYER_ID))
    {
      ProcessDefinition(geodatabase, topology);
    }

    static void ProcessDefinition(Geodatabase geodatabase, ArcGIS.Core.Data.Topology.Topology topology)
    {
      // Similar to the rest of the Definition objects in the Core.Data API, there are two ways to open a dataset's 
      // definition -- via the Topology dataset itself or via the Geodatabase.
      using (TopologyDefinition definitionViaTopology = topology.GetDefinition())
      {
        OutputDefinition(geodatabase, definitionViaTopology);
      }

      using (TopologyDefinition definitionViaGeodatabase = geodatabase.GetDefinition<TopologyDefinition>("Backcountry_Topology"))
      {
        OutputDefinition(geodatabase, definitionViaGeodatabase);
      }
    }

    static void OutputDefinition(Geodatabase geodatabase, TopologyDefinition topologyDefinition)
    {
      Console.WriteLine($"Topology cluster tolerance => {topologyDefinition.GetClusterTolerance()}");
      Console.WriteLine($"Topology Z cluster tolerance => {topologyDefinition.GetZClusterTolerance()}");

      IReadOnlyList<string> featureClassNames = topologyDefinition.GetFeatureClassNames();
      Console.WriteLine($"There are {featureClassNames.Count} feature classes that are participating in the topology:");

      foreach (string name in featureClassNames)
      {
        // Open each feature class that participates in the topology.
        using (FeatureClass featureClass = geodatabase.OpenDataset<FeatureClass>(name))
        using (FeatureClassDefinition featureClassDefinition = featureClass.GetDefinition())
        {
          Console.WriteLine($"\t{featureClass.GetName()} ({featureClassDefinition.GetShapeType()})");
        }
      }
    }
  }
}