They're modelling filaments as cylindrical tubes of hot electrons connecting pairs of galaxies. I don't know what you mean by "mass associated with filamentary

They're modelling filaments as cylindrical tubes of hot electrons connecting pairs of galaxies. I don't know what you mean by "mass associated with filamentary currents of energy", but while the electrons are hot (~million Kelvin), they're non-relativistic and their kinetic energy is negligible.