Relational Mobility and Social Network

Abstract

This paper presents an agent-based model that aims to model relational mobility in real life settings and explore the influence of relational mobility on social networks, specifically, the degree of connectivity, relationships strength, and interpersonal similarity. Relational mobility was modeled by two dimensions: the opportunity to form new relationships and the easiness to terminate existing relationships. Simulation results showed that high relational mobility resulted in higher the degree of connectivity and higher interpersonal similarity in social networks. The influences of relational mobility on relationships strength were inconsistent. The implication, limitation, and future directions of this model were further discussed.

Introduction

Social environments differ in the extent to which they afford opportunities for individuals to form new relationships and terminate existing relationships. Whereas living in some environments involves sustaining lifelong relationships with a small number of others, other environments involve brief or temporary social interactions with many people (Martin, Schug, & Maddux, 2019). The relevant concept—relational mobility—is defined as the general number of opportunities there are for individuals to select new relationship partners, when necessary, in a given social context (Schug et al., 2009). Whereas individuals in high mobility social context are frequently faced with opportunities to form new relationships, individuals in low mobility social context tend to be firmly embedded in their social network and have few opportunities to venture outside of current relationships and select new interaction partners (Schug, Yuki, Horikawa, Takemura, 2009).

It should be noted that relational mobility is not a characteristic of the personality or beliefs of individuals in a particular context, but rather describes the characteristics of the context (networks and social institutions) that surround each individual. As a results, most previous studies examining the influence of relational mobility typically examine relational mobility by measuring or manipulating individuals’ perceptions of how easy or difficult it is for people in their general social context to voluntarily move in and out of social relationships, rather than one’s own personal ability or desire to change relationships (Martin et al., 2019).

However, individuals’ perceptions of relational mobility of the context may be different from the actual characteristics of the context, considering the fact that individuals’ perceptions are easily influenced by their beliefs or personalities. To date, the actual relational mobility of the social context has scarcely been examined. Therefore, questions remain to be explored about the influence of actual relational mobility of the social context on interpersonal relationships or social networks, and whether the actual relationship mobility and individuals’ perception of relational mobility have consistent influence on social networks.

The current paper proposes using agent-based modeling (ABM) approaches to model the actual relational mobility of a social context. Agent-based modeling relies on realistic assumptions of interpersonal interactions and can enhance the understanding of the dynamics in social networks in real life settings (Gilbert & Nigel, 2009). A few agent-based models have been developed to explore the dynamics in social networks in previous studies (Watts & Strogatz, 1998; Barabàsi & Albert, 1999), but most of these studies fail to take the termination of existing relationships into consideration. The current paper presents an agent-based model which models the two core dimensions of relational mobility—opportunity to form new relationships and easiness to terminate existing relationships—in a social context. Using this agent-based model, we further explore the influence of relational mobility on social networks, specifically, the degree of connectivity, relationship strength, and interpersonal similarity in a social context.

Modeling and simulation

Individual agent properties

Agents in our model are a simplified abstracted version of people. Agents vary in their similarity with other agents. Agents in the same shape and color denotes similarity (see Figure 1). Similarity in our model can represent gender, ethnicity, political orientation, or other characteristics of people in real life settings. For the purpose of simplicity, the current model created three types of agents. The number of each type of agents ranges from 0 to 100 and can be changed at the beginning of modeling.

Each agent has two properties of interpersonal interactions: wiring probability (p₁) and ending probability (p₂). Wiring probability refers to the opportunity for individuals to form new relationships. In our model, each agent randomly chose an unlinked agent to create a link, the probability to successfully create the link is p₁. It should be noted that If the agent A failed to create a link with another agent B in this iteration, it is still possible that agent A will create a link with agent B in the next iteration.

Ending probability refers to the easiness for individuals to terminate existing relationships. In our model, agents are likely to be happy if they are linked with similar agents, but unhappy if they are linked with different agents. If agents are unhappy, they will end the existing link with different agents. However, agents differ in their tendency to be happy with similar links and the ability to end the existing links with different agents. This ability is determined by ending probability in our model. Specifically, If the percentage of existing links that connects similar agents to agent A is higher than p₂, then agent A is happy with his/her current relationships and will not end any existing link. If the percentage of existing links that connects similar agents to agent A is lower than p₂, then the agent A is not happy with his/her current relationships and will randomly choose an existing link to a dissimilar agent to end. It should be noted that wiring and ending probability are characteristics of a social context. Therefore, in a social context, every agent has the same level of wiring and ending probability, whereas social context can differ in the characteristics of wiring and ending probability.

Agent states and interaction rules

In our initial setup, no link has been created. First, a random agent A will create a link with another random agent B. Whether agents are creating a link or ending an existing link in the social context will then be randomly switched. Moreover, the probability to successfully create or end a link is determined by the wiring (p₁) and ending probability (p₂). It should be noted that if agent A ends the existing link with agent B in this iteration, agent A will not create a link with the agent B anymore in the future iteration. When agents are happy with their current relationships, they will not end any existing links with agents, but they will still try to create links with new and unlinked agents. The simulation will stop if all agents are happy and have tried to make links with all other agents.

Measures of social networks

Social networks are measured with three variables: the degree of connectivity, the relationship strength, and interpersonal similarity in a social context. The degree of connectivity refers to the total number of links between agents. The relationship strength refers to the average strength across all existing links. In our model, the strength is 0 if there is no link between two agents. Once two agents create a link between them, the strength becomes 0.1. After each iteration,

the strength will increase by 0.1 if the link is not ended. However, the strength will return back to 0 if the link is ended. Interpersonal similarity refers to the percentage of existing links that connect similar agents. It is calculated by the number of total links divided by the number of links that connects similar agents. Besides three variables measuring social networks, we also created a plot tracking the change of the number of happy agents in the social context across time.

Simulation results

Effects of end probability

We kept the population and wiring-probability constant and changed the value of end probability to observe effects of end probability on social networks. We compared the effects of low end-probability (e.g., 0.1 probability) to high end-probability (e.g., 0.9 probability). High end-probability yielded a lower number of total links, higher similarity among agents than low end-probability, and stronger link strength.

Effects of wiring probability

We kept the population and end-probability constant and changed the value of wiring probability to observe effects of end probability on social networks. We compared the effects of low wiring-probability (e.g., 0.1 probability) to high wiring-probability (e.g., 0.9 probability). High wiring-probability yielded more lower average link strength than low-wiring probability, but it wiring probability did not influence total links and similarity.

Effects of wiring and end probability

Next, both end- and wiring-probability were observed as being low (e.g., 0.1 probability) and high (e.g., 0.9 probability) simultaneously. The data for both high end- and wiring-probability yielded less total links, greater similarity among agents, and lower average strength of links.