Write mathematical report for Q$1$: Congratulations on your acceptance to the organising committee of the $2024$ CAB$203$ Bonkers tournament!

Bonkers is an extremely exciting and fictitious game.

There are many tasks that need to be done, which have been distributed amongst the organising committee

members. Your acumen with discrete structures is well known, and hence you have been assigned several

organisational tasks which will benefit from some computerisation.

All tasks are intended to make significant use of graph theoretic tools and problems.

$1.$ The tournament structure needs to be set; that is to say, who plays who. For this tournament a

structure is used where all games are set at the beginning. Another committee member will propose

the tournament structure and your job is to determine whether it has the required properties. The

committee has determined that the following properties are sufficient:

$$ For every pair of distinct players, either they play against each other, or there are at least two

other players that they both play against.

$$ All players have the same number of games.

So for example, if Alice and Bob don$$t play against each other then it$$s still OK as long as they both

play against two players in common, say, Charlie and Denise.

Your job is to find a method that, given a tournament structure, determines whether the above properties hold.

Implement your method in a Python function like so:

def gamesOK $($ games $)$:

where games is a set of proposed games to play, given as pairs of players, like so:

games $=\{("$ Alice $","$ Bob $"),("$ Charlie $","$ Bob $")\}$

Note that the order of the players in a particular game does not matter: $(\text{'}$Alice$\text{'},$'Bob'$)$ specifies

the same game as $(\text{'}$Bob$\text{'},$'Alice'$).$ You may assume that in the games given no player plays against

themselves, every player plays in at least one game, there is at least one player, and no game is given

more than once.

Your function should return True if the required property holds for the games given, otherwise False.