Olympic Logic

Alice, Becky, Charlotte, Daphne, Elsie and Fran decide to hold their own Modern Pentathlon competition. For the fencing segment, each competitor has to play one match against every other competitor. A match results is either a win or a loss. Can you deduce what all of the results were?

• No competitor lost all their matches, but one person won all their matches.
• Daphne won her match against Becky.
• Alice and Elsie won the same, odd, number of matches, but Alice lost to Elsie.
• Becky and Fran won a total of seven matches
• Charlotte won only one game, against the only other person who also won only one game.