Galaxies form chains (filaments) that connect groups and clusters of galaxies. The filamentary network includes nearly half of the galaxies and is visually the most striking feature in cosmological maps. We study the distribution of galaxies along such a filamentary network, trying to find specific patterns. Our galaxy filaments are defined using the Bisous process. We use the two-point correlation function and the Rayleigh $Z$-squared statistic to study how the galaxies are distributed along the filaments. We show that galaxies and galaxy groups are not uniformly distributed along filaments, but tend to form a regular pattern. The characteristic length of the pattern is 7~$h^{-1}$Mpc. A slightly smaller characteristic length 4~$h^{-1}$Mpc can also be found, using the $Z$-squared statistic. One can say that galaxy filaments are like pearl necklaces, where the pearls are galaxy groups distributed more or less regularly along the filaments. We propose that this well defined characteristic scale could be used as a cosmological test.