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

{
  await 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"] = " ";

          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();
    }
  });
}