public IReadOnlyList<TopologyEdge> GetEdges()

// 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 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 ...
      }
    }
  }
}