Emergence of communities and diversity in social networks

Abstract

Communities are common in complex networks and play a significant role in the functioning of social, biological, economic, and technological systems. Despite widespread interest in detecting community structures in complex networks and exploring the effect of communities on collective dynamics, a deep understanding of the emergence and prevalence of communities in social networks is still lacking. Addressing this fundamental problem is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in society. An elusive question is how communities with common internal properties arise in social networks with great individual diversity. Here, we answer this question using the ultimatum game, which has been a paradigm for characterizing altruism and fairness. We experimentally show that stable local communities with different internal agreements emerge spontaneously and induce social diversity into networks, which is in sharp contrast to populations with random interactions. Diverse communities and social norms come from the interaction between responders with inherent heterogeneous demands and rational proposers via local connections, where the former eventually become the community leaders. This result indicates that networks are significant in the emergence and stabilization of communities and social diversity. Our experimental results also provide valuable information about strategies for developing network models and theories of evolutionary games and social dynamics.

Keywords: communities; fairness; networks; social diversity; ultimatum game.

Fig. 1.

Evolution of proposals in the treatment and control groups. (A–D) The proposers’ offers $p$ from round 1 to round 60 in the two treatment groups, T1 (A) and T2 (B), and the two control groups, C1 (C) and C2 (D), respectively. The mean value and the SD of $p$ in each of the 60 rounds are denoted by circles and column bars, respectively. The average value of $p$ in T1 is slightly higher than in the other groups, and the SD of $p$ in T1 and T2 is much larger than that in C1 and C2. The results demonstrate that whether a structured network is regular or random has little effect on the average fairness of proposers, whereas the diversity in proposers, reflected by the SD, is remarkably promoted by network structure, in contrast to the two control groups with random interactions.

Fig. 2.

Spatiotemporal patterns of proposers. (A and B) Spatiotemporal patterns of the proposers’ offers $p$ in the two treatment groups T1 and T2. (C and D) Spatiotemporal patterns of the proposers’ offers $p$ in the two control groups C1 and C2. The ordinate represents the spatial orders of proposers. Two proposers with most common neighbors will be adjacent to each other. The color bar represents the value of $p$. In A and B, neighboring proposers gradually form some local communities that can be distinguished by different colors (different values of $p$). The communities are stable as reflected by the presence of relatively clear and invariant boundaries among the communities after a number of rounds (e.g., 30 rounds in A). Each community is composed of some neighboring proposers who offer similar $p$ as represented by a similar color. By contrast, in C and D, there are no local communities and a single homogeneous community of proposers with similar values of $p$ as represented by a similar color arises. The local communities with different internal agreements in T1 and T2 account for the diversity in proposers. By contrast, in C1 and C2, the absence of local communities and the homogeneity of proposers account for the relatively small SD of proposals.

Fig. 3.

Local communities of proposers. (A and B) A snapshot of the proposers’ offers $p$ and the responders’ $q$ in round 60 for (A) T1 with a regular network and for (B) T2 with a random network. The subjects are arranged in two rings, where the outside ring represents proposers and the inside ring represents responders. The color bar represents the value of $p$ and $q$. Communities are highlighted by colored boxes. The arrangement of proposers is the same as in Fig. 2 (two subjects with most common neighbors are adjacent to each other) but with periodic boundary conditions. The regular network offers a natural sequential order but there is no such order for the random network. We assign the spatial order of the nodes in random networks by using a simulated annealing algorithm. The order is exclusively based on the topology rather than the acts of subjects. (C) The evolution of a fairly stable community in T1. The snapshots of the community in four rounds are shown. The responder can be regarded as a “leader” of this community and is followed by the four neighboring proposers. In round 16, the responder’s minimum acceptance level $q$ was relatively low and all neighboring proposal $p$s were accepted. In round 29, the responder’s $q$ was increased and all neighboring $p$s were rejected. Because the proposers are relatively rational, they gradually increased their $p$s to make deals with the responder. In round 32, three proposers made deals by enhancing their $p$s, and a proposer’s $p$ is higher than the responder’s $q$. In round 33, all of the proposers made deals with the responder and their $p$s were equal to or slightly higher than the responder’s $q$.