As @user207421 say there is no way to know the current state of the connection because of the TCP/IP Protocol Architecture Model. So the server has to notice you before closing the connection or you check it by yourself.
This is a simple example that shows how to know the socket is closed by the server:
sockAdr = new InetSocketAddress(SERVER_HOSTNAME, SERVER_PORT);
socket = new Socket();
timeout = 5000;
socket.connect(sockAdr, timeout);
reader = new BufferedReader(new InputStreamReader(socket.getInputStream());
while ((data = reader.readLine())!=null)
log.e(TAG, "received -> " + data);
log.e(TAG, "Socket closed !");