We consider random competitive or cooperative symmetric interactions of N agents, thus N(N-1)/2 links,on a fully connected network. A constraint is introduced such that the network contains an equal number of competitive and cooperative interactions. This constraint imposes an additional implication: only (square)matrix sizes (4k x 4k) or ((4k+1) x (4k+1)), where k is a positive integer, can be considered. The full configuration structures of this ensemble of networks is investigated. This is carried out by analysing the averaged eigenvalue distribution of the finite N sized random sign symmetric matrix ensemble (RSSME). The results from simulation studies are presented and compared to simulation results for the average eigenvalue distribution of the RSSME without the equality (50/50) constraint. Applications in the domain of competitive and cooperative interaction structures of agents on financial markets are outlined.

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