Dual diagrams

Just as links join pairs of nodes in a diagram, it can be said that nodes join pairs of links. If links were drawn as nodes and conversely, a new diagram, called the dual, could be established. Sometimes a dual is more concise than the original; and sometimes it just reveals its information in a more desirable form.

 
Figure 5: The dual of a diagram lets links be nodes.  

• The tail-head factorization
• Duals and homomorphism
• The head-tail factorization
• Counting paths
• Eigenvalues and eigenvectors