The G3 non-isomorphic clustering graph and the problem of the physical reality of the clustering tendency

Chains ofnormal galaxies dominate small-scale clustering. This filamentary structure has nothing to do with large-scale filaments between clusters; and the revelation of short galaxy chains among normal galaxies was not expected by Arp, who investigated chains ofpeculiar galaxies. The nature of revealed chains cannot be explained in terms of so-called filaments observed in a scale of 100 Mpc: there is no continuation between 100 kpc and 100 Mpc chains of galaxies. Three sorts of clustering modes, corresponding toG ₁,G ₂ andG ₄ non-isomorphic graphs withthree vertices, are free of the time paradox. Chains (the clustering mode corresponding to theG ₃ graph) are stable on a time scale less (tens and sometimes a hundred times) than the conventional age ofnormal galaxies. Why do the chains dominate small scales?