It's several years later, and the Edge browser now uses Chromium as its rendering engine.
Checking for IE 11 is still a thing, sadly.  
Here is a more straightforward approach, as ancient versions of IE should be gone.
if (window.document.documentMode) {
  // Do IE stuff
}
Here is my old answer (2014):
In Edge the User Agent String has changed.
/**
 * detect IEEdge
 * returns version of IE/Edge or false, if browser is not a Microsoft browser
 */
function detectIEEdge() {
    var ua = window.navigator.userAgent;
    var msie = ua.indexOf('MSIE ');
    if (msie > 0) {
        // IE 10 or older => return version number
        return parseInt(ua.substring(msie + 5, ua.indexOf('.', msie)), 10);
    }
    var trident = ua.indexOf('Trident/');
    if (trident > 0) {
        // IE 11 => return version number
        var rv = ua.indexOf('rv:');
        return parseInt(ua.substring(rv + 3, ua.indexOf('.', rv)), 10);
    }
    var edge = ua.indexOf('Edge/');
    if (edge > 0) {
       // Edge => return version number
       return parseInt(ua.substring(edge + 5, ua.indexOf('.', edge)), 10);
    }
    // other browser
    return false;
}
Sample usage:
alert('IEEdge ' + detectIEEdge());
Default string of IE 10:
Mozilla/5.0 (compatible; MSIE 10.0; Windows NT 6.2; Trident/6.0)
Default string of IE 11:
Mozilla/5.0 (Windows NT 6.3; Trident/7.0; rv:11.0) like Gecko 
Default string of Edge 12:
Mozilla/5.0 (Windows NT 10.0; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/39.0.2171.71 Safari/537.36 Edge/12.0 
Default string of Edge 13 (thx @DrCord):
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/46.0.2486.0 Safari/537.36 Edge/13.10586 
Default string of Edge 14:
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/46.0.2486.0 Safari/537.36 Edge/14.14300 
Default string of Edge 15:
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/52.0.2743.116 Safari/537.36 Edge/15.15063 
Default string of Edge 16:
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/58.0.3029.110 Safari/537.36 Edge/16.16299 
Default string of Edge 17:
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/64.0.3282.140 Safari/537.36 Edge/17.17134 
Default string of Edge 18 (Insider preview):
Mozilla/5.0 (Windows NT 10.0; Win64; x64; ServiceUI 14) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/64.0.3282.140 Safari/537.36 Edge/18.17730 
Test at CodePen:
http://codepen.io/gapcode/pen/vEJNZN