In mathematics, specifically complex analysis, a multivalued function has often the property that, near almost every point, the graph of the function is the disjoint union of one or several graphs of smooth functions, which are called branches of the multivalued functions. In the case of complex analytic functions, these branches can be prolongated to smooth functions that are defined in the whole complex plane except a finite number of points, and are equal to one value of the multivalued function in their domain. Often, a branch refers value specifically to such a maximal branch.