  We study the structure of the underlying network of connections in the
Minority Game. There is not an explicit interaction among the agents, but they
interact via global magnitudes of the model and mainly through their
strategies. We define a link between two agents by quantifying the similarity
among their strategies, and analyze the structure of the resulting underlying
complex networks as a function of the number of agents in the game and the
value of the agents' memory, in games with two strategies per player. We
characterize the different phases of this system with networks with different
properties, for this link definition. Thus, the Minority Game phase
characterized by the presence of crowds can be identified with a small world
network, while the phase with the same results as a random decision game as a
random network. Finally, we use the Full Strategy Minority Game model, to
explicitly calculate some properties of its networks, such as the degree
distribution, for the same link definition, and to estimate, from them, the
properties of the networks of the Minority Game, obtaining a very good
agreement with its measured properties.
