The preceding heap has this property:

• For every node other than a leaf, its key value is less than (or equal to) that of its children.

(A heap could also be arranged so that the key of every node is greater than that of its children.)

Compare this property to the binary search tree property:

• For every node other than a leaf, its key value is greater than (or equal to) the key of every node in its left sub-tree and less than (or equal to) the key of every node in its right sub-tree (Example).

The binary search tree property imposes a total ordering on all of its nodes.

The heap property imposes a partial ordering on all of its nodes, but a total ordering on the nodes of each branch.