Elites Power Network

Disecting the Anatomy of Twitter Elites

Overview

The ease of access to information on social ties through online social networks and advances in computing in the past 15 years has allowed researchers to study large social networks. However, our fascination with big data has lead to us to neglect one import aspect of social networks, namely the elite network. While social scientist has spent a great deal of attention in the past century, not much research has been done on this topic recently.
In this research we analyze the structural properties of Twitter elite network and its sub-structures. We define elites as accounts with largest number of followers. We use the induced follow and retweet graph of Twitter elite in our analysis. We start with the induced graph of 500 elite accounts, and study the structural changes as the network expands to more elites. We identify groups of tightly connected accounts, using consensus clustering based on the many runs of non-deterministic community detection algorithm. These identified elements show substantial social coherence, and many of them could have not been identified using well known community detection algorithms. Moreover, we found that although expansion coincide with increase in density, the sub-structural properties of the network remain stable. Finally, we pay great detail to individual accounts, as we identify important elites, using follow relations and retweets. We find these super-elites to be of different types when focusing on different relations.

Identifying the Elite Network

One critical question "how to define elites". Our main criteria for elites in Twitter is their number of followers. With this definition the elite network is the set of N most followed accounts and the follow relations among them. The second important question is "How large is N". In order to find the right N, we consider different values and study different views of the elite network.

Expanding the Elite Network

First we study the macro level structure of different views, by looking at their strongly connected components. Examination of these views using Sankey diagram visualization shows that:

Communities of Elites

When examining graph representations of networked systems (e.g., social networks, biological networks), a popular approach is to try and identify different “communities” (i.e., groups of nodes that satisfy certain inter- and intra-group connectivity properties) in an attempt to glean insight into the fine structure of the systems under study. This approach is greatly facilitated by a number of popular community detection (CD) algorithms. A curious feature of many of these CD algorithms is that different runs of a single algorithm typically results in often vastly different sets of communities. This intriguing and at the same time troubling observation raises the question whether these detected communities have any “meaning” beyond satisfying certain level of goodness with respect to connectivity.
To minimize the effect of non-deterministic variations in the identified communities, we adopt the following strategy: We run Combo community detection technique on each view of the elite network n times and determine the communities that individual nodes are mapped to in each run in a vector with n values, called ‘community vector’. Then, we group all the nodes that are consistently (i.e., all n times) mapped to the same community (i.e., have the same community vector) and refer to such a group as a Stable Element. Clearly increasing n is more restrictive which may lead to smaller stable elements since more runs can simply split an element to two (or more) smaller ones. We conservatively consider n = 100 in our analysis. This process also results in groups of nodes for which no other node has the same community vector. We group to this last set of nodes and nodes in stable elements with a size smaller than 10 and refer to them as Unstable Element.

Elites & their Communities

We organize communities and elites in the following interactive tables: Our analysis on social and geo footprint of communities show a high level of homogeneity among users.

Community-Level Structure of Elite Network

The identified communities give a unique opportunity to summarize the elite network. For each view we summarize the graph by showing all the nodes in one community as a single circle whose size is proportional to the size of the community. When then connect circle i to j with a directed link that show number of follower of community i that are in community j. This in turn shows the level of interest of community j in community i. In the following plots, we did not include self loops (i.e., followers in the same community) due to their large number. Our result show:
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How do Communities Expand?

We also consider the effect of expansion of the community level structure of elite network. Therefore, we keep track of the communities' individual nodes in each view. This in turn reveals the overlapping users between two communities in consecutive views and shows the similarity of two communities in different views. Our visualization using Sankey Diagram show that the majority of nodes in communities of each view stick together to make up communities in the next view. The social and geo footprint of related communities in different views show that the theme of most communities remains the same across different views. while the theme for some other communities slightly evolves as more nodes join the community or two communities merge together.

Of coarse, the evolving theme for some communities are due to the arrival of many new nodes in each view of the elite network. To verify this issue, we expanded the views of the elite network by 20% in each step and observed that any change in the theme of individual community occurs very slowly. This visualization nicely shows the effect of network expansion on identified communities.

Who Influences Elites?

We use three metrics to measure influence in the elite network.

Use the table of influence measures to brows through our findings. Click on the following plots to interact with the graph.

PageRanke Influence
Retweet Influence
Reply Influence
Please refer to our Technical Report for more information.

Team Members