How People Interact in Evolving Online Affiliation Networks

The study of human interactions is of central importance for understanding the behavior of individuals, groups, and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links, and we analyze quantitatively the tendencies used to create ties in these evolving online affiliation networks. We show that an accurate estimation of these probabilistic tendencies can be achieved only by following the time evolution of the network. Inferences about the reason for the existence of links using statistical analysis of network snapshots must therefore be made with great caution. Here, we start by characterizing every single link when the tie was established in the network. This information allows us to describe the probabilistic tendencies of tie formation and extract meaningful sociological conclusions. We also find significant differences in behavioral traits in the social tendencies among individuals according to their degree of activity, gender, age, popularity, and other attributes. For instance, in the particular data sets analyzed here, we find that women reciprocate connections 3 times as much as men and that this difference increases with age. Men tend to connect with the most popular people more often than women do, across all ages. On the other hand, triangular tie tendencies are similar, independent of gender, and show an increase with age. These results require further validation in other social settings. Our findings can be useful to build models of realistic social network structures and to discover the underlying laws that govern establishment of ties in evolving social networks.

Popular Summary

The concept of social networks, in the age of Twitter and Facebook, seems like a really banal one. Social networks, however, have turned out to be a fertile ground for scientific studies of human interactions by not only social scientists, but also by physicists, from which we gain illuminating insights about ourselves and our societies. For example, why, and how, do we make new friends or establish fresh social ties? In this paper, we show that meaningful answers to these questions can be learned, by bringing concepts and methods from statistical physics to bear in a new analysis of the detailed growth dynamics of two networks associated with two online social-networking sites.

Although human beings differ from each other as individuals, our motivations for finding new friends or creating new social ties can in fact be classified into a small number of categories. For example, we make friends because they are the friends of our friends, or because we want to benefit from their popularity, or because we want to create a new friendship circle outside our current acquaintances. These mechanisms leave characteristic patterns in a social network, but the dynamic nature of the network quickly scrambles the patterns. This realization leads us to depart from the standard methods of study of network-dynamics, which are based on analysis of a series of snapshots of an evolving network. Our approach, enabled by the single-action temporal resolution of the social-networking data, monitors and assigns a known motivation or mechanism to every single tie-seeking action of each individual involved.

Our statistical analysis reveals a number of important and interesting facts about human behavioral traits. In the social-networking communities that we have studied, women reciprocate messages three times as much as men, and this difference increases with age. Men tend to connect with the most popular people more often than women across all ages. The tendency of forming new ties through the friend-of-a-friend mechanism is, however, independent of gender, but increases with age. Our results also make a methodological point: They cannot be inferred from other statistical methods that primarily focus on snapshots of a growing network.

We expect to see many new research activities grow out of our study, including verifications of our conclusions in other sociological contexts as well as generalizations of our method to other evolving complex networks such as protein-interaction networks in biology.

Figure 1

(a) The five probabilistic tendencies we used to classify the interactions. Black arrows indicate existing links and red arrows are the possible options for a new link, according to the following tendencies: (1) social exchange, which corresponds to establishing a reciprocal link, i.e., add as favorite someone who has already added us to their favorites lists; (2) balance, where we select a favorite who is in the list of one of our existing favorites (friend of a friend); (3) distant connection, where the connection is to a member with whom there is no proximity, i.e., one needs at least three links to reach this member; (4) collective action, where we connect to a person whose connectivity is well above the average connectivity in the community (we quantify this behavior by examining whether the total degree of the receiving agent belongs to the upper 5% of the degree distribution at the given time); and (5) structural hole, where a link connects two otherwise not connected clusters of at least three members each, and which are otherwise not directly linked to each other (in the picture this link would connect the cluster of people in hats with the red-haired cluster). (b),(c) Why we cannot extract tendencies from a static snapshot: In the presented example a triangle relation is built from time $t-2$ to time $t$ under two different scenarios that lead to the same resulting triangle. (b) The ties X-Y and Y-Z can be formed, at times $t-2$ and $t-1$, respectively, via distant mechanisms resulting in a balance mechanism for the formation of X-Z at time $t$. Here X uses a friend of a friend to be introduced to Z. (c) A different path, though, would classify the X-Z tie differently. If X connects to Z before connecting to Y, then the X-Z link represents a distant tendency, since there are no close connections between them. A static network analysis would suggest that X used balance to connect to Z, instead.

Figure 2

The relative appearance of the five probabilistic tendencies in the actions of the community members in QX using favorites (red), in QX using guest book (green), and in POK using guest book (blue). These tendencies are compared to a completely random selection (yellow). Exchange and balance are practically nonexistent in random selections, but carry significant weight in the interactions of the real communities. Connecting to distant members appears in the community much less frequently than in random, while the preference towards well-connected agents (collective action) is significantly more prominent. Finally, the structural hole is significantly suppressed in the real communities compared to the randomized case.

Figure 3

Probability of different tendencies, based on self-reported gender in the QX community in favorites list interactions. Exchange and structural hole are significantly more frequent in females compared to males.

Figure 4

Variation of the average tendency percentage with the self-reported age of the QX members. (a) The exchange tendency decreases with age. (b) The balance tendency is sharply increasing with age in younger ages, and slowly declines for ages above 20 years. We do not observe any strong dependence on age for (c) collective action or (d) structural hole (bottom right). The insets show the differences between males and females of the same age for each tendency.

Figure 5

Fraction of the appearance of a tendency as a function of the adding member’s list size, at the time of addition. Qualitatively, all three data sets are in agreement with each other. The small quantitative differences may be due to the different means of interaction and/or the design of each platform.

Figure 6

(a) Histogram of the number of members as a function of the links that they initiated (x-axis) and the links that were pointed to them but initiated at the partner’s side (y-axis). (b–d) Average percentage of exchange, balance, and distant mechanisms as a function of the links initiated and received.

Figure 7

Comparison of the probabilistic tendencies fraction, where links are characterized either at the time of addition (solid lines) or at the time of observation (dashed lines) in the POK community.

Figure 8

Probabilistic exchange tendencies extracted from static network snapshots for several directed networks.