Each box below is a Tree struct. Each Tree's child pointer is its first child in a linked list of direct children. The subsequent child in the list is the current child's sibling. Each child has a pointer back to its parent.
The rank, k, of each node is the rank of the tree below that node if you consider that node a root.
This entire diagram represents a rank 2 or degree 2 binomial tree. The Node pointers on each Tree are omitted for simplicity.
+---------+
+----->k: 2 |
| +---------+
| |parent |
| |sibling |
| +--+child |
| | +---------+
| |
| | +---------+ +---------+
| +-->k: 0 | +------>k: 1 <--+
| +---------+ | +---------+ |
+-----+parent | | +----+parent | |
| |sibling +-+ | |sibling | |
| |child | | +--+child | |
| +---------+ | | +---------+ |
| | | |
+-------------------+ | |
| +---------+ |
+-->k: 0 | |
+---------+ |
|parent +--+
|sibling |
|child |
+---------+
A Heap contains a standard library doubly linked list where the Value for each list Element is a pointer to a Tree.