The fingerprint of educational platforms in social media: A topological study using online ego-networks

Copyright Alexandru Topirceanu, Dragos Tiselice, Mihai Udrescu

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A case study on Liga AC's Facebook friendship network

Towards the end of 2014 I have finalized a rather innovative approach towards social media analysis. Together with co-researchers Dragos Tiselice and Mihai Udrescu, a challenge was launched to analyze "if" and 'how" educational platforms are mirrored on online social platforms. To that end, we have used the ego-network (direct friendships) of Liga AC, a student volunteering organization in Politehnica Timisoara. Extracting the data with netvizz and analyzing it with Gephi and a some of Mathematics, we have reached the following results.

We highlight four detected communities that form the friendship network of Liga AC. Through empirical analysis we conclude that the red community (28.4% of nodes) is formed by students from the Computer Science department (2010-2014), namely they are colleagues of the league members. The blue community (26.9% of nodes) are other volunteers at national level, mostly from cities like Bucharest of Cluj-Napoca. The yellow community (24.7% of nodes) are student volunteers from other leagues originating from the same city and/or the same university (e.g. Mechanics, Electronics, Electro-energetics, Chemistry, Medicine). Finally, the green cluster (19.6% of nodes) is formed by the actual Liga AC members. It consists of actual core members, older members and close friends.

The spatial layout of the network also makes sense since the green cluster (Liga AC members) is overlapping on one side with the red one (daily colleagues). Underneath, there is a form of professional interaction with other students from the same city. Finally, in the lower part there is the blue cluster of other young volunteers at the national level.

Metrics Analysis

If we look at the upper half of Table 1 we observe the specific values of the graph metrics for average users of socializing platforms. In comparison, the Liga AC networks does show a specific fingerprint. First, it has a very large average degree which might indicate that many friends of Liga AC know each other. However, the low density and the high modularity denote the fact that we are dealing with a highly clustered network. High modularity translates into a powerful community structure. Second, the clustering coefficient strengthens the first observation in the sense that most links are local: friends know friends found in their proximity, but not distant ones. Third, the path length is small and characteristic for social networks, together with the diameter, so we conclude upon the fact the Liga AC is a very well structured network, with many intra-community edges and very few inter-community edges.

Centrality analysis

Moving on to centralities, the first notable and characteristic aspect is that all four different centrality measures overlap in terms of the detected nodes with high centrality. While this aspect might not seem relevant, it is very uncommon for social networks to have any nodes in their topology which result as important independent of the centrality algorithm used. To explain this further, each of the four mentioned state of the art centrality measures is based on a different algorithm (e.g. degree, random walks, shortest paths), thus it is normal for specific nodes to surface as more important depending on the measure used. However, and, to the best of our knowledge, the phenomenon observed on the Liga AC network is unique. The fact that a specific and independent proportion of nodes are central regardless of the centrality algorithm used is interpreted through the fact that those few nodes (roughly 10, see Figure 2d) are the roots of the communication and bridges between the volunteering organizations at a local level. Empirically, we have observed that these nodes are former presidents of the league, or current project leaders. This handful of people shape the very existence of Liga AC and related leagues.

To conclude, we create a similarity analysis between LigaAC's network and the other 3 online models. Based on previous work, we can say the following about each social platform:

• Twitter networks are topologically heterogeneous and present many random long range links because of the follower concept. They have no notable community structure and a very short average path length.

• Google Plus networks are topologically homogeneous and present a powerful community structure with very few inter-community ties because of the circle concept. They have a high average path length and a high modularity.

• Facebook networks are the more balanced topology, with structured communities which overlap on the boundaries. They have preferential attachment in terms of degrees, a short path length and realistic clustering.

Discerning over the obtained results, we can conclude that the fingerprint of educational networks is completely dissimilar with Twitter networks, has a slight similarity to Facebook friendship networks, but is mainly a good replica of the homogeneous Google Plus networks. The emerging community structure resembles very much the one resulting from the circle concept introduced by Google.

Copyright Alexandru Topirceanu, Dragos Tiselice, Mihai Udrescu

11.01.2015