A connection game is a board game in which players compete to develop or complete a type of topological connection with their pieces. This could involve forming a path between two or more locations, completing a closed loop, gathering pieces into a single group, etc. Note that the geometry of the connection is not important for a game to be classified a connection game, but rather only fact that the winning of the game relies on forming some sort of connection (Browne 2005, p. 3).
Note that tic-tac-toe, connect-four, and any other games involving patterns of specific size or shape are not strictly connection games (Browne 2005, p. 9).