Institutions or organizations sometimes have a hard time determining the quantity and quality of their impact. For example, institutions for educational outreach might need a way to quantify how far their program have reached the community and how significant these impacts are. Companies concerned with the cooperation of its employee might need a way to quantify how each employee interact with each other, the quality of these interaction, and how it can affect the company. This is all the question of network, or social network, if you may say.
Talking about social network might remind us of Facebook. Sometimes an ad might pop up, or maybe a friend suggestion of people you don’t know. But if we think about it carefully, those ads or the friends suggestion are not randomly assigned for us. It closely reflects our circle, who we know and in what context we know these people, which in turn give insight on our interests, daily routine, or even deepest, darkest secrets.
There is a science for analyzing interaction and relationship between people, called social network analysis. Social network analysis is a study on the interaction and relationship between entities within a defined network. This study encompasses mapping, measuring, and analyzing different parameters in the relationship, as well as how information flow within the network. The entities in questions does not have to be individual; they can be groups, organizations, or even inanimate objects, so long as there are perceived interaction or relationship between them. Since being proposed in the beginning of 20th century, Social Network Analysis has grown to be an independent field with its own methodology and parameter.
The aim of SNA goes beyond descriptive measure; as explained by Wasserman and Faust (1994), its main purpose leans toward understanding and answering question. I can safely say us corporate slaves at one point in our career probably have personal experience with seemingly harmless interpersonal interaction affecting the progress of the organization as a whole. According to Wasserman and Faust, that is what SNA does; understanding the structure and patterns of these relationship and discover how it affect other people and the organization. R
elationship and interaction are inherently built within organization; regardless of what fields the organization is working on. Butts (2008) specifically describe the field of social network as interdisciplinary, which pointed out the characteristic of SNA as being applicable in diverse fields.
THE MATHEMATICAL BACKGROUND
Social network can be represented in many ways, but the more popular and visually appealing way to do it is using ‘web’ that we commonly see in graph theory. These networks are built by ‘nodes’ connected by ‘links’, in which the nodes represent entities, while the links represent relation between them.
Interestingly enough, graph theory actually acts as mathematical representation for social network analysis. But before we get into that, let’s talk about the definition boundary of some of the terminologies we mentioned above. According to Butts (2008), ‘entities’ in this case must be distinct from one another, can be uniquely identified, and are finite in number, while ‘relation’ must be defined on a pair of entities and there are ‘dichotomous qualitative distinction’ between relations that are present and those that are absent.
Under this constraint, social network can be represented as graph. In graph theory, graphs are built by ‘edge’ and vertex’, in which an ‘edge’ indeed can connect only a pair of ‘vertex’. This definition fits our need considering the definition of relation and entities we discussed above.
Many constants and units in graph theory can also be used to represent parameters in social network, for example the order of a graph (the number of vertex), if we put it in the context of social network, represent the size of the network and the number of people in it. A ‘loop’ (edge going out from a vertex back to itself) represent reflective relationship, while ‘multiplex’ graph are those with more than one edge connecting two vertices.
This article will only talk about graphs without ‘loop’ and are not ‘multiplex’, also known as ‘simple graph’. This explanation might not be adequate to give full insight on the role of graph theory in SNA, however it is enough to cover the basic on why graph theory is suitable to represent network data. Another option to represent network data is to use matrix (Wasserman and Faust, 1994), which will not be discussed here.
WHAT INFORMATION CAN WE GET FROM IT
Social Network analysis represented as graph gives information beyond the fact that two people represented by connected nodes regularly talks to each other. Does this mean the more nodes and links in the graph, the better? Does more contact for each person means more benefit for the for the organizations? Turns out, it is not always the case. Let’s see some key parameters which are the focal interests of SNA, i.e. degree centrality, betweenness centrality and closeness centrality. For this purpose, I am going to use the ‘Kite Network’ (figure 1) developed by David Krackhart (Rozental & Helman, 2008) and a graph (figure 2) from an article by Cross (2011).
Figure 1: Kite Network developed by Krackhardt
Figure 2: Illustration by Cross (2011)
Degree centrality means the number of direct connections a node has. At a glance, it might look like the more connection you have the better. However, what really matters is where those connections lead to and how they connect the isolated network members. For example, look at Diane in Figure 1. She has the most number of connections in her network, however all of the contacts she has are those who already know each other. It means Diane only stays in one clique, therefore only in the same circle of information.
Betweenness centrality stated the importance of a node in determining whether an information will flow or do not flow in the network. In the previous case, Susan and Diane both have high degree centrality, yet their impact to the organization as a whole will be different, due to this parameter. Diane has high degree centrality yet if she disappears, the people she connected to will still be able to access the information because they are connected to each other.
On the other hand, Susan in graph 2 also has high degree centrality, yet she connects to people who are not connected to each other. This means, aside from getting a lot of new information, Susan’s position is also very important, because if she disappears, all the network falls apart.
High betweenness centrality does not have to come with high degree centrality. Take a look at Heather (figure 1). She has small number of contacts, but her position is really important because without her, Ike and Jane will be cut from the circle. Ted (figure 2) also has similar characteristics, low degree centrality with high betweenness centrality.
This notion is in line with the result by Gray, Parise, and Iyer (2011) on the role of SNA in helping employees become more innovative. They found that more innovative employee do not have bigger network, but instead they have more ‘bridging ties’ aka ties that connect them to employees who are otherwise unconnected. Closeness centrality means how well a node can pose at the center point of a network. Being a center point means being equidistant to both ends of network and therefore being in the best position to monitor the flow of information in the network. This is best represented by Fernando and Garth in figure 2.
Butts, C. T. (2008). Social network analysis: A methodological introduction. Asian Journal of Social Psychology, 11(1), 13–41. https://doi.org/10.1111/j.1467-839X.2007.00241.x
Cross, R. (2011). The Most Valuable People in Your Network. Retrieved from https://hbr.org/2011/03/the-most-valuable-people-in-yo
Gray, Parise, & Iyer. (2011). Innovation Impacts of Using Social Bookmarking Systems. MIS Quarterly, 35(3), 629. https://doi.org/10.2307/23042800
Rozental, D. & Helman, T. (2008) SNA: Social Network Analysis. Retrieved from http://www.kmrom.com/Site-En/Articles/ViewArticle.aspx?ArticleID=144
Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Application. Social Networks. Cambridge University Press
Part 2 SNA in Education
Part 3 SNA: Step by Step