The analysis of societies demonstrates the recurrent nature of small world topology in the interactions of elements in such worlds. The small world topology proves to have beneficial properties for system's performance in many cases, however there are also scenarios where the small world topology's properties negatively affect the system's outcome; thus in depth knowledge on the small world weaknesses is needed in order to develop new generations of artificial societies and new models of economic systems. In this paper, a multi-agent system based on request for proposal protocol and coalition formation organisational paradigm is used to analyse properties of small world social networks of agents. Experiments center on nodes in the network with high betweenness and in particular the distribution of agents in the population across these nodes. Results show that small world topology scenarios lose their beneficial properties when non-competitive agents are positioned as high betweeness nodes in the network.