We introduce a new representation scheme for coalitional games, called coalition-flow networks (CF-NETs), where the formation of effective coalitions in a task-based setting is reduced to the problem of directing flow through a network. We show that our representation is intuitive, fully expressive, and captures certain patterns in a significantly more concise manner compared to the conventional approach. Furthermore, our representation has the flexibility to express various classes of games, such as characteristic function games, coalitional games with overlapping coalitions, and coalitional games with agent types. As such, to the best of our knowledge, CF-NETs is the first representation that allows for switching conveniently and efficiently between overlapping/non-overlapping coalitions, with/without agent types. We demonstrate the efficiency of our scheme on the coalition structure generation problem, where near-optimal solutions for large instances can be found in a matter of seconds.