Graffiti on property that you do not own is classed as a crime (vandalism). See this link.
This is a gallery of graffiti tags extant in our area. If you know the person responsible, you should report that to police (British Transport Police if it's on railway property). Do you have CCTV and has it shown any culprits?
Siemens cabinet on Longstone Rd near crossing.
wall of 320 Lanark Road
north wall around entrance to tunnel under canal (Scottish Canals)
low wall by bridge in Slateford (CEC)
On stone wall in Easter Hailes Gate (CEC)
graffiti inside bridge 5 (Kingsknowe Road Bridge) (CEC)
graffiti on bridge (Kingsknowe Road Bridge)(CEC)
Kingsknowe Drive sign (at west end)
Virgin Media cabinets off Longstone Place.
Litter bin in Kilncroftside