public class Relationship : ArcGIS.Core.CoreObjectsBase, System.IDisposable  

public async Task CreatingARelationship()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file"))))
        using (RelationshipClass relationshipClass = geodatabase.OpenDataset<RelationshipClass>("LocalGovernment.GDB.OverviewToProject"))
        using (FeatureClass projectsFeatureClass = geodatabase.OpenDataset<FeatureClass>("LocalGovernment.GDB.CIPProjects"))
        using (FeatureClass overviewFeatureClass = geodatabase.OpenDataset<FeatureClass>("LocalGovernment.GDB.CIPProjectsOverview"))
        {
            // This will be PROJNAME. This can be used to get the field index or used directly as the field name.
            string originKeyField = relationshipClass.GetDefinition().GetOriginKeyField();

            EditOperation editOperation = new EditOperation();
            editOperation.Callback(context =>
      {
          // The rows are being added to illustrate adding relationships. If one has existing rows, those can be used to add a relationship.
          using (RowBuffer projectsRowBuffer = projectsFeatureClass.CreateRowBuffer())
          using (RowBuffer overviewRowBuffer = overviewFeatureClass.CreateRowBuffer())
          {
              projectsRowBuffer["TOTCOST"] = 500000;

              overviewRowBuffer[originKeyField] = "LibraryConstruction";
              overviewRowBuffer["PROJECTMAN"] = "John Doe";
              overviewRowBuffer["FUNDSOUR"] = "Public";

              using (Row projectsRow = projectsFeatureClass.CreateRow(projectsRowBuffer))
              using (Row overviewRow = overviewFeatureClass.CreateRow(overviewRowBuffer))
              {
                  Relationship relationship = relationshipClass.CreateRelationship(overviewRow, projectsRow);

                  //To Indicate that the Map has to draw this feature/row and/or the attribute table has to be updated
                  context.Invalidate(projectsRow);
                  context.Invalidate(overviewRow);
                  context.Invalidate(relationshipClass);
              }
          }
      }, projectsFeatureClass, overviewFeatureClass);

            bool editResult = editOperation.Execute();
        }
    });
}