In complex analysis, a branch (also called a sheet) is a portion of the range of a multivalued function over which the function is single-valued. Combining all the sheets gives the full structure of the function. It is often convenient to choose a particular branch of a function to work with, and this choice is often designated the "principal branch" (or "principal sheet").

In graph theory, a branch at a point  in a tree is a maximal subtree containing  as an endpoint (Harary 1994, p. 35).

REFERENCES:

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.

Lu, T. "The Enumeration of Trees with and without Given Limbs." Disc. Math. 154, 153-165, 1996.

Schwenk, A. "Almost All Trees are Cospectral." In New Directions in the Theory of Graphs (Ed. F. Harary). New York: Academic Press, pp. 275-307, 1973.