Broadcast receiver for checking internet connection in android app

Answer to your first question: Your broadcast receiver is being called two times because

You have added two <intent-filter>

1. Change in network connection :
   <action android:name="android.net.conn.CONNECTIVITY_CHANGE" />

2. Change in WiFi state:
   <action android:name="android.net.wifi.WIFI_STATE_CHANGED" />

Just use one:
<action android:name="android.net.conn.CONNECTIVITY_CHANGE" />.

It will respond to only one action instead of two. See here for more information.

Answer to your second question (you want receiver to call only one time if internet connection available):

Your code is perfect; you notify only when internet is available.

UPDATE

You can use this method to check your connectivity if you want just to check whether mobile is connected with the internet or not.

public boolean isOnline(Context context) {

    ConnectivityManager cm = (ConnectivityManager) context.getSystemService(Context.CONNECTIVITY_SERVICE);
    NetworkInfo netInfo = cm.getActiveNetworkInfo();
    //should check null because in airplane mode it will be null
    return (netInfo != null && netInfo.isConnected());
}