How to make bootstrap 3 tab nav active by default?

You also need to specify the active class on the default tab-pane (and for fading tabs you need to add the in class), thus you should change

<div class="tab-pane fade" id="graduation">

to

Bootstrap 3

<div class="tab-pane fade in active" id="graduation">

Bootstrap 4

<div class="tab-pane fade show active" id="graduation">

Bootstrap 4

<div class="tab-pane fade show active" id="graduation">
<div class="tab-pane fade" id="graduation">

Bootstrap 3

<div class="tab-pane fade in active" id="graduation">
<div class="tab-pane fade in" id="graduation">