a graph and label its white vertex by and the remaining black vertices with . Associate a labelled coordinate k to each of the vertices, representing the continuous degrees of freedom associated with that particle. The coordinate 0 is reserved for the white vertex With each bond linking two vertices associate the Mayer f-function corresponding to the interparticle potential Integrate over all coordinates assigned to the black vertices Multiply the end result with the symmetry number of the graph, defined as the inverse of the number of permutations of the black labelled vertices that leave the graph topologically invariant. The first two cluster integrals are {| | || || |- | || || |} The expression of the second virial coefficient is thus: where particle 2 was assumed to define the origin (). This classical expression for the second virial coefficient was first derived by Leonard Ornstein in his 1908 Leiden University Ph.D. thesis. See also Boyle temperature - temperature at which the second virial coefficient vanishes Excess virial coefficient Compressibility factor References Further reading http://scitation.aip.org/content/aip/journal/jcp/50/10/10.1063/1.1670902 http://scitation.aip.org/content/aip/journal/jcp/50/11/10.1063/1.1670994 Reid, C. R., Prausnitz, J. M., Poling B. E., Properties of gases and liquids, IV edition, Mc Graw-Hill, 1987 Statistical mechanics