Fig 1.
Social networks that arise when newcomers use popularity to guide their selection of friends.
Starting with Euler in 1736, the study of network topology has been couched in terms of graph theory, which represents individuals as nodes (drawn here as green circles) and a connection between two individuals as an edge between two nodes (green lines). Together, the nodes and edges define a graph. The arrangement of the nodes on the page is nonessential; what matters is who links to whom. The networks shown here were constructed through a process in which the newcomer samples m times (without replacement) from the distribution defined by Eq 1 and links up with whomever is selected [1]. Each network began as a complete (i.e., fully-connected) graph with m+1 nodes (open circles) and grew with the arrival of newcomers (filled circles).
Fig 2.
A visualization of a social network, used as the stimulus in the experiment.
The image appeared to the participants exactly as it appears to you, the reader.
Fig 3.
Individual differences in sensitivity to popularity when selecting whom to befriend.
(A) Distribution of the best-fit value of L across participants. (B) Correlation between the best-fit values of L for a participant's first and second selections, fit separately.
Fig 4.
The structure and connectivity of a growing network depends on the policy used by a newcomer when selecting its connections.
(a) The degree distribution specifies how likely it is for a person to have a particular number of connections. These are the degree distributions for three networks that vary only in the standard deviation of L across the population (10,000 individuals, L = 1, m = 3). Introducing individual differences bends the degree distribution away from being a straight line, the signature of a scale-free network. (b) Another measure of network connectivity that is affected by the variability is the characteristic path length—the average distance between individuals. Notice the interaction between the direction of the effect and the value of L with no effect of individual differences at L = 1. (c) A third affected measure of network connectivity is the local clustering coefficient, the proportion of possible connections among one’s friends that actually exist, averaged across all people. We tested mean values of L between –5 and 5 in steps of 0.25, and standard deviations of L between 1 and 4 in steps of 0.25. Each combination of parameter values was run once, with m = 3 and 10,000 nodes.