How placing limitations on the size of personal networks changes the structural properties of complex networks

Abstract

People-to-people interactions in the real world and in virtual environments (e.g., Facebook) can be represented through complex networks. Changes of the structural properties of these complex networks are caused through a variety of dynamic processes. While accepting the fact that variability in individual patterns of behavior (i.e., establishment of random or FOAF-type potential links) in social environments might lead to an increase or decrease in the structural properties of a complex network, in this paper, we focus on another factor that may contribute to such changes, namely the size of personal networks. Any personal network comes with the cost of maintaining individual connections. Despite the fact that technology has shrunk our world, there is also a limit to how many close friends one can keep and count on. It is a relatively small number. In this paper, we develop a multi-agent based model to capture, compare, and explain the structural changes within a growing social network (e.g., expanding the social relations beyond one's social circles). We aim to show that, in addition to various dynamic processes of human interactions, limitations on the size of personal networks can also lead to changes in the structural properties of networks (i.e., the average shortest-path length). Our simulation result shows that the famous small world theory of interconnectivity holds true or even can be shrunk, if people manage to utilize all their existing connections to reach other parties. In addition to this, it can clearly be observed that the network's average path length has a significantly smaller value, if the size of personal networks is set to larger values in our network growth model. Therefore, limitations on the size of personal networks in network growth models lead to an increase in the network's average path length.