Carbinelength

Carbinelength is a hypothetical metric used in chemical graph theory and materials science to describe the connectivity of carbon-containing networks. The term suggests a length scale derived from bond topology rather than direct physical measurement, and it is not a standard, universally adopted quantity in mainstream chemistry.

Definition and calculation: For a given molecule or material, extract the carbon-only subgraph by considering carbon atoms as nodes and covalent carbon–carbon bonds as edges. Carbinelength, denoted L_C, is defined as the mean shortest-path distance between all unordered pairs of carbon atoms in this carbon subgraph, measured in number of covalent bonds (i.e., the average geodesic distance). In variant formulations, the distance can be weighted by bond order, or converted to a physical length by associating each edge with an average C–C bond length to yield a value in angstroms. A normalized version divides the sum by the maximum possible number of pairs or by (N_C − 1), where N_C is the number of carbon atoms.

Interpretation and uses: L_C provides a topology-based sense of how “spread out” carbon atoms are within a structure. Topologies that are highly crosslinked or branched tend to have smaller L_C, while linear or sparse networks yield larger values. It can be used to compare polymers, nanocarbon materials, or other carbon-rich systems in a purely graph-theoretical way, supplementing more conventional physical measurements.

Limitations: Carbinelength is not a standard physical length and depends on how the carbon graph is defined and weighted. It should be used cautiously and in concert with established metrics such as bond lengths, densities, and mechanical properties. Related concepts include average path length and graph diameter.