Online social network analysis method

The first quantitative analysis method to be evaluated was a thorough online social network analysis. This method provides insight into the structure and the development of the networks. Relationships between individuals are analyzed and significant individuals within the online social networks are identified (Hennig et al., 2012). There are software tools to support data analyses. Several statistics, filters, and layouts help to understand the online social network structures. There are general network metrics which indicate the overall network structures, or focus on sub-networks in comparison to the entire network. Edge metrics focus on the path lengths of the edges between individual nodes and indicate the distance of relationships. And finally, there are node metrics which investigate the characteristics and indicate the importance of individual nodes within the network. Filters help to focus on sub-networks, and layout settings help to visualize the social networks. The following sections illustrate conventional measurement techniques of online social network analysis, including common statistics, filters, and layouts.

3.1.1.1. Statistics

Statistical online social network measures can indicate the structure of a network. Specific metrics can be used as indicators for measuring social capital in social networks. These statistical measures have mainly been applied to offline social networks. Within this research, these statistics were used to describe online social networks. From this

perspective, they were computed and evaluated as indicators for measuring social capital. The following sections introduce existing indicators and describe potential practical interpretations of these indicators based on former research. First, general network metrics are delineated, then, more specific edge and node metrics are described. These are commonly used statistical indicators for analyzing social networks.

General network metrics

The graph density describes the actual network compared to the complete network, which would have all possible edges. A complete network has a density equal to 1 (Gephi, 2011a; Heymann, n.d.). Hennig et al. (2012) define graph density “as the ratio of the number of edges to the number of dyads, i.e., the ratio of the number of actual to possible edges.” (p. 118). The denser a graph is, the faster (potential) information spread in the network, as more communication relationships among nodes exist.

The modularity detects communities within a network (Blondel, Guillaume, Lambiotte & Lefebvre, 2008; Gephi, 2011b; Heymann, n.d.). A high modularity score is an indicator for an advanced internal community structure of the network. It describes the division of the network into sub-networks which might also be present in the offline world (Blondel et al., 2008; Newman, 2006). In how far this is the case, would have to be investigated in further research. It is not part of this particular research to test this proposition. The modularity basically shows the fraction of edges of the sub-networks

39 minus the expected fraction of a random edge distribution (Newman, 2006)3. A high score on modularity means there are dense connections between nodes of a sub-network which only share sparse connections with nodes of other sub-networks. A high modularity score does not per se imply a high number of sub-networks (Blondel et al., 2008;

Lambiotte, Delvenne & Barahona, 2009).

The measure of connected components identifies sub-graphs in which all nodes are connected through a path and which are not connected to other sub-graphs

(Heymann, n.d.). The algorithm developed by Tarjan (1972) is able to identify strongly and weakly connected components in directed networks (Gephi, 2011c).

Finally, within the general network metrics, the diameter of the graph shows the maximal “distance between all pairs of nodes” (Heymann, n.d., p. 15; Brandes, 2001; Gephi, 2011d). Hennig et al. (2012) define a graph´s diameter as “the longest shortest path of any dyad” (p.143). The smaller the network diameter is, the faster information (potentially) reaches the farthest node over the longest distance via the shortest paths. Edge metrics

The edge metric of the (average) path lengths describes the (average) distance between all pairs of nodes, with connected nodes having a distance equal to 1 (Brandes, 2001; Gephi, 2011e; Heymann, n.d.). The measure of path lengths is the basis for the diameter metric as well as node centrality measures of betweenness centrality and closeness centrality.

Node metrics

Freeman (1979) provided a conceptual framework for centrality measures. In general, centrality metrics are supposed to indicate the structural importance of individuals within the network (Hennig et al., 2012). They are to “express a structural advantage,

importance, or dominance” (Hennig et al., 2012, p. 124). One could refer to absolute values to describe how important one node is within a network of a specific size. One disadvantage of absolute values is that they depend on a network´s size and make it difficult to compare two networks of different sizes. If such a comparison is a research objective, centrality measures can be normalized [0,1]. Then, each centrality value is divided by the sum of all centrality values of that network. This approach provides relative scores which can be compared across different networks (Hennig et al., 2012).

A node´s degree is described by the number of adjacent edges (Gephi, 2011f; Heymann, n.d.; Kadushin, 2012). In-degree represents incoming edges, whereas out- degree shows outgoing edges of a node. The degrees are supposed to be an indicator of an individual´s activity or involvement. Therefore, degree is evaluated as a measure for centrality, as activity and involvement might express a structural advantage (Hennig et al., 2012). Important individuals in a social network can be identified based on their degrees.

40 The betweenness centrality shows the number of times “a node appears on shortest paths between nodes in the network” (Heymann, n.d., p. 16; Brandes, 2001; Brandes, 2008; Gephi, 2011g; Kadushin, 2012). Freeman (1977) introduced betweenness centrality as an indicator for the control of an individual over the communication flow within the network (Newman, 2005).

Closeness centrality measures “the average distance from a given node to all other nodes in the network” (Heymann, n.d., p. 16; Brandes 2001; Brandes 2008; Gephi, 2011h; Kadushin, 2012; Sabidussi, 1966). Closeness centrality is supposed to indicate how long it will take to disseminate information from a given node to all other nodes (Newman, 2005).

The eccentricity measure is a by-product of the centrality measures based on path distance. Node eccentricity shows the maximal distance from a given node to the farthest node from it in the network.

The eigenvector centrality metric assigns a score indicating importance to nodes, based on their connections to other nodes of importance (Gephi, 2011i). Eigenvector centrality increases as the node is connected to other central nodes (Heymann, n.d.).

The clustering coefficient of a node indicates how complete its neighborhood is (Gephi, 2011j; Heymann, n.d.). The algorithm was developed by Latapy (2008) and was based on theory by Watts and Strogatz (1998) who used this measure to identify small- world networks. The clustering coefficient indicates the integration of a node into the structure surrounding it, and thus, indicates the level of cohesion on the node level (Hennig et al., 2012). The average clustering coefficient applies to the entire network and is defined by the mean value of individual coefficients (Latapy, 2008).

3.1.1.2. Layouts

In online social network analysis, it is useful to visualize these networks for further investigation. A visualization of online social networks can illustrate underlying structural patterns within the network. In graph visualization tools, there are many different layout settings to create a readable graph (Bastian et al., 2009). For instance, the Force-Atlas 2 layout is a force-directed algorithm which calculates nodes´ repulsion on the basis of a Barnes-Hut calculation (Barnes & Hut, 1986; Heymann, n.d.). This layout allows for preventing overlap of nodes and adjusting node sizes and colors based on different node metrics, such as degree, modularity class, or centrality measures. Edges can be adjusted by size and color as well. Furthermore, nodes and edges can be labeled, and label overlap can be ruled out.

3.1.1.3. Filters

For more detailed investigations of, for instance, underlying structural patterns of online social networks, it is also practical to create sub-networks for focusing on specific

characteristics of these sub-networks. Different filters are available to produce sub- graphs of the network, which allows for a more in-depth analysis of those sub-graphs

41 (Bastian et al., 2009; Heymann, n.d.). For instance, ego-networks can be created to

analyze sub-networks referring to important individuals within the complete online social networks. There are filters to help understand the development of an online social

network in time. Furthermore, more filters and various possibilities to highlight specific sub-networks can be used based on many different network characteristics (Bastian et al., 2009; Heymann, n.d.). As these sections showed, online social network analysis is an appropriate research method for investigating the overall and more specific structures of online social networks. Within this research method, there are many options for

researchers to focus on different levels of these networks, from the macro level of analyses of whole networks, via meso levels of analyses as to sub-networks, to the micro level of analyses regarding individuals. When it comes to identify more specific underlying relationship patterns of online social networks, another method is commonly used: the triad census. The triad census method is a social network analysis method which adds supplemental findings to the analyses illustrated in this sub-chapter. The next sub-chapter introduces this method in further detail.