mutual
Shared equally between people, with feelings or actions both ways.
Mutual means shared between two or more people or groups, where everyone involved feels or does the same thing toward each other. When two friends have mutual respect, each one respects the other. When the feeling is mutual, both people feel the same way.
The word captures something important about balanced relationships. If you admire someone but they don't admire you back, that admiration isn't mutual. But when you and your best friend enjoy each other's company equally, you have a mutual friendship. Countries can have mutual agreements where both sides promise to help each other. Sports teams can be mutual rivals, with each one seeing the other as their main competition.
You'll often hear the phrase “the feeling is mutual” when someone wants to show they feel the same way. If you tell a teammate “Great working with you!” and they respond, “The feeling is mutual,” they're saying they also enjoyed working with you.
A mutual friend is someone you and another person both know. If you meet someone new and discover you both know the same person, that's a mutual friend connecting you. The word emphasizes the two-way nature of the connection: it goes both directions, not just one.