I think Buu's digest cycle watch is genius. Thanks for sharing. As others have noted $interval also causes the digest cycle to run. We could for the purpose of auto logging the user out use setInterval which will not cause a digest loop.
app.run(function($rootScope) {
var lastDigestRun = new Date();
setInterval(function () {
var now = Date.now();
if (now - lastDigestRun > 10 * 60 * 1000) {
//logout
}
}, 60 * 1000);
$rootScope.$watch(function() {
lastDigestRun = new Date();
});
});