The maintenance of altruism among selfish individuals is studied
by considering an evolutionary prisoner's dilemma game where 
the players are located on the sites of different networks. 
The players can follow one of the two strategies (cooperation and defection)
and try to maximize their income, coming from games with the neighbors, 
via the adoption of the strategy of the more successful
neighbors meanwhile irrational choices (noise) are allowed. 
The cooperators die out in the zero noise limit for those connectivity
structures which cannot be spanned by overlapping triangles.
In these cases the frequency of cooperators has a maximum 
at an optimum value of noise resembling stochastic resonance.
     In the opposite cases the frequency of cooperators decreases 
when increasing the magnitude of noise and/or the temptation 
to choose defection. It is conjectured that the frequency 
of cooperators is enhanced when reducing the number of long loops 
in the connectivity structure. Due to a proper mechanism 
the cooperation is prevented effectively by inhomogeneities 
appearing either in the number of neighbors or in the activity 
of learning.