If it's a free to play game, I'm not sure how you can protect against someone creating a new account. But integrating highscores with social networks may discourage people from creating multiple accounts as it would be linked to their profile. While also making the highscore more meaningful to be competitive against friends.
The highscore should be the highest score from a single match. If you want to have a running total or average they should be ranked separately. Likely the average should be further divided by number of games played so it's clear that the people with the most games played and the highest average are truly superior players.
Also highscore boards can be a daily highscore (for that day or the previous day) and all-time highscore.