  In this dissertation, we analyze the computational properties of
game-theoretic centrality measures. The key idea behind game-theoretic approach
to network analysis is to treat nodes as players in a cooperative game, where
the value of each coalition of nodes is determined by certain graph properties.
Next, the centrality of any individual node is determined by a chosen
game-theoretic solution concept (notably, the Shapley value) in the same way as
the payoff of a player in a cooperative game. On one hand, the advantage of
game-theoretic centrality measures is that nodes are ranked not only according
to their individual roles but also according to how they contribute to the role
played by all possible subsets of nodes. On the other hand, the disadvantage is
that the game-theoretic solution concepts are typically computationally
challenging. The main contribution of this dissertation is that we show that a
wide variety of game-theoretic solution concepts on networks can be computed in
polynomial time. Our focus is on centralities based on the Shapley value and
its various extensions, such as the Semivalues and Coalitional Semivalues.
Furthermore, we prove #P-hardness of computing the Shapley value in
connectivity games and propose an algorithm to compute it. Finally, we analyse
computational properties of generalized version of cooperative games in which
order of player matters. We propose a new representation for such games, called
generalized marginal contribution networks, that allows for polynomial
computation in the size of the representation of two dedicated extensions of
the Shapley value to this class of games.
