public bool IsLinkChartView {get;}

{
  var mv = MapView.Active;
  // check the view
  var isLinkChartView = mv.IsLinkChartView;

  // or alternatively get the map and check that
  //var map = MapView.Active.Map;
  // check the MapType to determine if it's a link chart map
  var isLinkChart = map.MapType == MapType.LinkChart;
  // or you could use the following
  // var isLinkChart = map.IsLinkChart;
}

{
  var mapPanes = FrameworkApplication.Panes.OfType<IMapPane>().ToList();
  var mapPane = mapPanes.FirstOrDefault(
      mp => mp.MapView.IsLinkChartView && mp.MapView.Map.Name == "Acme Link Chart");
  var lcMap = mapPane.MapView.Map;
}