The thermodynamics and kinetics of cross-linking reactions between PAHs of various reactive edge types that are observed in soot precursors are explored using density functional theory. The forward rate constants confirm that reactions involving aryl sigma-radicals are faster than others, but rate constants for reactions between aryl sigma-radicals and localized pi-radicals can be as large or even larger than for two aryl sigma-radicals. However, rates for all cross-linking reactions between small PAHs are likely too slow to explain soot formation. The equilibrium constants show that reactions involving sigma and pi-radical PAHs are the most favorable at flame temperatures. Equilibrium constants for larger PAHs show that the ability to form bonded-and-stacked structures results in enhanced equilibrium constants for the reaction of two large localized pi-radicals compared to those for other edge types. This suggests that combined physical and chemical interactions between larger pi-radical PAHs could be important in flame environments.