Complex sentence: The area is right on the periphery of the City of Glasgow local authority boundaries, and is near to Bearsden which although part of the Glasgow conurbation is outwith those boundaries (being instead part of the East Dunbartonshire council area).
Split into simpler sentences: The area is right on the periphery of the City of Glasgow local authority boundaries, and is near to Bearsden. Part of the Glasgow conurbation is outside those boundaries (being instead part of the East Dunbartonshire council area).