Dyadic relations enjoy yet another form of graph-theoretic representation as labeled bipartite graphs or labeled bigraphs.  I’ll just call them bigraphs here, letting the labels be understood in this logical context.

The figure below shows the bigraphs of the 16 dyadic relations on two points, adopting the same arrangement as the previous displays of binary matrices and loopy digraphs.

References

• Peirce, C.S. (1880), “On the Algebra of Logic”, American Journal of Mathematics 3, 15–57.  Collected Papers (CP 3.154–251), Chronological Edition (CE 4, 163–209).
• Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.  Volume 3 : Exact Logic, 1933.
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.  Volume 4 (1879–1884), 1986.

Resources

• Peirce’s 1870 Logic Of Relatives