Network exchange theory (NET) predicts differences in the resource accumula
tions of positions in interconnected groups of actors. The theory distingui
shes between two types of networks-strong and weak power. To date only a fe
w studies have tested the theory under weak power conditions. In the presen
t research we investigate six line networks that contain elements of both s
trong and weak power. Line networks have been particularly, important in th
eories of social exchange and the importance of linear exchange is frequent
ly reflected in natural settings. Four of the investigated lines are longer
than any previously studied. We introduce new experimental features design
ed to minimize extraneous factors, thereby optimizing the translation of st
ructural power differences into observable profit differentials. Results ge
nerally support the idea that longer lines may contain elements of both str
ong and weak power. Most notably, while positions identified as high strong
power do obtain approximately 70% or more of resources, there is evidence
that a nonzero likelihood of exclusion in the central position of the 7-lin
e may decrease its power.