As is the fulfillment of many mitzvot, The Brit Milah too is ritual that should be performed in the presence of a minyan, a quorum of ten adult Jewish males (Over the age of Bar Mitzvah,  thirteen). Celebrating this mitzvah with friends and family glorifies the name of God, as it says, "Berov am hadrat Melech," the larger the attendance, the greater is the honor to the King (God).