This seems to parallel the cycle of the Holly King and the Oak King, who each rule one half of the year: Hekate carries the torch through the dark half of the year, while Brigid takes it for the light half. Some suggest that Hekate and Brigid are sisters who share the torch." --http://www.fortunecity.com/marina/pontoon/2457/id110.htm
All this may seem very odd, given that Hekate is Greek and Brigid Celtic. But traditional beliefs that evolve over time may have little to do with historical origins. Both Goddesses are very ancient, and have been worshipped in Britain for centuries, so who is to say what relationship may have developed between them? Sometimes the ways my Greek and Celtic beliefs over lap is rather surprising. . .