# Social Network Relationships and Structures

Q £ Frequently consider the connection of all things in the universe.

Marcus Aurelius

In this chapter, many of the fundamental network relationships and structures are presented in the context of information spread through social media linked individuals and groups. Core social networks relationship terminology, such as symmetry, directionality, intermediary relationships, and network complexity are addressed. Relationship structures, such as dyadic, triadic, and balanced relationships are also summarized in simple terms. The concept of homophily and filter bubbles as communication echo chambers are described using a modern example: the dwindling trust in mass media. The chapter concludes with an overview of several popular social network visualization and analysis software tools. These tools are useful for exploring and understanding the relationships and structures presented in this chapter as well as in social network analysis.

## Social Network Relationship Overview

In social network analysis, each community member is treated as a node, and their communication with other members is treated as a link or connection between nodes. Social networks are analyzed at varying scales, but the primary purpose of social network analysis is to ultimately utilize mathematical models to study the structure, development, and evolution of the social network [31]. Fundamental to social network analysis is its structure, as that will dictate the efficiency by which information can be spread throughout a social network group. The advantage of a social network analysis method of examining social media groups is its ability to quantify relationships mathematically. Social network analysis preliminaries are discussed further in the next chapter.

## Core Social Network Relationships

Critical to the discussion of modern information spread is the concept and influence of social networks. First, let us define a general network. A network is a set of objects or nodes along with a mapping or description of the relationship between the nodes [32]. A social network, then, is a set of individuals related in some way so that their relationship can be mapped or traced.

### Symmetry

Consider the most basic case of two friends: a symmetric relationship, in which two friends are linked to each other as shown in Figure 4.1. In this case, individuals 1 and 2 are linked within a social network. Specifically, they are symmetrically linked because each has two-way mutual communication with the other. In traditional human interactions, this is the most common social network mapping of a face-to-face communication between friends. Formally, this mapping of individuals is called a “sociogram”.

FIGURE 4.1: Individuals 1 and 2 in a simple symmetric relationship.

### Directionality

In Figure 4.2, a third individual is added to the network. Notice that the new actor, individual-3 has a symmetric relationship with individual-1, but is only singularly directional to individual-2. This directional-sensitivity in a network relationship is known as directionality. Perhaps individual-3 is a writer. While individual-2 is being influenced by the information spread from individual-3 as he reads his work, individual-3 has no direct knowledge of or contact with individual-2, while individual-! is acquainted with and talks to both of the remaining people.

### Intermediary Relationships

What happens if a fourth individual who is only acquainted with individual- 2 enters the network map as shown in Figure 4.3? While individual-4 and individual-3 are symmetrically linked, she has no direct relationship to others

FIGURE 4.2: A three-node relationship mapping of individuals 1,2, and 3.

in the network. She is said to have an “intermediary relationship” to the rest of the network. In this case, the intermediary is individual-2 who serves as her link to the rest of the social network.

FIGURE 4.3: Individual 2 acts as an intermediary.

### Complex Networks

As more people are added to a social network, their interrelationships become increasingly complex. Notice the variety of symmetric and unidirectional relationships in Figure 4.4. By only adding a few more people to our social network, each with their relationship links, the social network has grown complex enough that it proves difficult to trace and predict how information might spread between individuals on opposite sides of the network map.

In the next sections, we will address social networks in more detail about their structure and formalized descriptive elements.

FIGURE 4.4: A simplified complex social network.

## Homophily and Filter Bubbles

Meaning “love of the same”, homophily is a term coined in the context of social theory by Lazarsfeld and Merton in 1954 [33]. Mainly, it expresses the concept that similar individuals (or groups of individuals) tend to be drawn together within networks, with closer similarities resulting in closer network bonds. Likewise, people or groups with dissimilarity will tend toward involvement in completely separate social networks. Additionally, these network groups often induce positive feedback into themselves due to similarities between members, making the group “likeness” bonds increasingly stronger [32].

In a modern popular social media context, this phenomenon is often known as a filter “bubble” [34]. Similar to the concept of a social “echo chamber”, a social filter bubble is the isolation of individual thoughts, perceptions, and news from opposing viewpoints due to their current belief systems, social media circles, and internet search tendencies. Evolving non-transparent technology has made filter bubbles increasingly intense, as personalized news streams, ads, and searches begin to dominate typical internet activity. Growing concern has arisen as to whether this trend is harming democratic ideals as these concepts enter public consciousness [35] following the recent, social media internet attributed, 2016 United States presidential election results. Additionally, the knowledge of the existence of fake news and filter bubbles has eroded some public trust in traditional television, newspaper, and internet journalism. The graph in Figure 4.5 exemplifies an increasing trend of widespread distrust of mass media over the years in the United States.

FIGURE 4.5: U.S. trust in mass media trends. Courtesy of [36].

In the realm of sociology, the most straightforward grouping consists of two individuals, also known as a dyad. An example of this might be a teacher and a student. Both have a connection to one another, as they interact with and influence others within a small two-person network. In the case of the teacher- student example, there exists “reciprocity”, between the two individuals for the reasons mentioned above. In personal interactions, dyadic reciprocity is frequent. Still, once online social media interactions enter the picture, it is not hard to imagine several typical situations in which non-reciprocal relationships dominate. For example, consider an internet blogger with several hundred followers. The blogger may follow and reply to some of her readers, but for the most part, the blogger is not interacting with the readers, and the relationship is purely one-sided. Returning to the teacher-student dyadic relationship, if the teacher lectures material and the student does not actively participate in course discussion (if any), then there exists no reciprocity in the relationship. In networking terms, these relationships can be called “directed”, as there is a one-sided, non-mutual connection between the individuals.

Let us expand the simple person-to-person relationship to three individuals, each existing within the same network. With the addition of a third person, network analysis can truly begin because a society (however small) has emerged [37]. A “triad” forms with the introduction of the third individual, and the complexity of the relationships is considerably increased. Consider three individuals: person A, B, and C. Person A is a good friend with person В. reciprocally. Person C is friend with person В but does not know person A: however, person C follows the blog posts of person A due to common interest but is not reciprocally followed.

FIGURE 4.6: Example of a simple triad relationship.

As the network grows in size by even a small amount, it becomes more complicated due to the reciprocity of relationships, the presence or lack of intermediaries, and the number of individuals within the network group. For further understanding, the concept of balance can be considered. Balance within a triad network can lie formalized as follows: “In the case of three entities, a balanced state exists if all three relationships are positive in all respects, or if two are negative and one is positive” [38]. It can further be argued that groups naturally tend toward these balanced triad states. As an example, consider a triad where two individuals dislike the third triad member. It is likely then that the two disliking members will like one another, perhaps due to shared ideologies or opinions that cause them both to dislike the third person of the network. Eventually, the third person may even become isolated from the group or network entirely [32].

Social Network Analysis Software

TABLE 4.1: Social network analysis and visualization tools.

 Software Features Cuttlefish detailed visualizations, interactive manipulation, TeX support Cytoscape data integration, analysis, and visualization, plug-in support Gephi interactive visualization for complex networks and systems, dynamic graphs, open-source NetworkX create, manipulate, and study complex networks, Python package, random network generation NodeXL Microsoft Excel template, open-source, explore network graphs, social network specific plug-ins R general purpose analytics, extensive libraries for social network analysis SocNetV analysis and visualization, user-friendly, network construction, cross-platform, open-source

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## Social Network Analysis Software

Several social network visualization and analysis software tools exist to aid in understanding and interpreting data collected from social media systems. Some of the major packages and tools for social network visualization and analysis are shown in Table 4.1. Applications of such software includes usage in sociolog}-, finance, biology, network theory, and more. It can be argued that the usage of modern software is not only useful, but required. The complexity of many networks (sometimes with several thousands of nodes or more) makes unassisted visualization and analysis impossible.

Consider Figure 4.7, a randomly generated network of fifty nodes, each representing an individual in a social network. These network sociograms were created with the widely used Social Network Visualizer software (SocNetV). A snapshot of the tool user interface is found in Figure 4.8.

Note that the nodes in the network vary significantly in relation to one another. Some nodes are sparsely connected, others are very dense and connected to several neighbors. Additionally, clusters of nodes in close connection and proximity are also visually apparent .

Figure 4.9 gives reports on the network degree of centrality and clustering of nodes.

For many network development and analysis software tools, random networks can be created given user-input parameters. Specific data can also be imported for the visualization and analysis of real-world data sets. Readers are encouraged to try one or more of these tools to create random networks or importing data to get a sense of visually identifying clustering, density, degree centrality, polarization, and other metrics.

FIGURE 4.7: Randomly generated fifty-node network.

FIGURE 4.8: User interface for the Social Network Visualizer tool.

FIGURE 4.9: Social Network Visualizer: centrality and clustering.

## Exercises

• 1. Provide an example of a filter bubble in the context of modern-day geopolitics.
• 2. Give an example of a dyadic relationship. Does reciprocity exist in your example?
• 3. Consider Figure 4.6 as a sample triad relationship. Discuss the concepts of reciprocity and balance in this context .
• 4. Filter bubbles are of increasing concern for mass communication and socialization in a digital media age. Give an example of a filter bubble one might encounter and draw a sociogram of your example. Identify the major nodes that influence information spread within your sample network.
• 5. Choose a software tool from Table 4.1 (or a similar tool of your choosing). Generate a random 100-node directed small world network. Once your network is developed, generate a degree centrality report and determine the adjacency matrix.