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Minamoto was a surname given by the Emperors of Japan for members of the imperial family who were excluded from the line to become next Emperor and lowered into the ranks of the common lords since 814. The Minamoto was the most powerful clan of all four great clans that dominated Japanese politics during the Heian, Kamakura, Muromachi and Edo periods in Japanese history. The other three were the Fujiwara, the Taira, and the Tachibana.
The Minamoto clan is also called the Genji (源氏, "Minamoto clan"), or sometimes the Genke (源家, "House of Minamoto"), using the On'yomi readings of gen (源) for "Minamoto", while shi or ji (氏) means "clan", and ke (家) is used to read "extended family".
The Taira, their rival were actually Emperor descendant too which make them Cousin to the Minamoto.