"Oxidation Numbers in the Study of Metabolism"
Ronald Bentley, James Franzen, and Thomas G. Chasteen
BIOCHEMISTRY AND MOLECULAR BIOLOGY EDUCATION
Vol. 30, No. 5, pp. 288–292, 2002
I find that it is sometimes helpful to sum the oxidation numbers of individual carbon atoms, but I am not sure that it is necessary to do so. Consider the reaction catalyzed by propanediol dehydratase, which is the conversion of propane-1,2-diol to propionaldehyde (propanal), as discussed in the reference above. One carbon increases in oxidation number and another decreases, but there is no net oxidation or reduction of the whole molecule.
EDT
I may have misunderstood your question. When a carbon atom is joined to another carbon atom, both atoms have the same electronegativity, and one of the atoms cannot be said to own both electrons, unlike a C-O bond, for example.