Temporal Networks

Analysis of Twitter as a temporal network

Social networking services have become a huge part of our lives. We use them to establish and maintain an online presence and connect with other individuals with whom we share hobbies or our daily coffee. And although social networking services have been around for some time now, there is still much that we don’t know about them. Do they share the same structure and properties with real social networks, the ones we form through daily interaction, or do the possibilities of the internet allow them to expand beyond this scope?

Social networks fall into the classification of temporal networks since their structure evolves with time. Temporal network models view the network as a series of graphs where the users are the nodes, while interactions among the users form the edges of the graphs. Since Twitter is the focus of this project, the term “follower” can be used to define connections between the users. Namely, we consider that user A is connected to user B, for as long as user A is following user B.

Snapshot of a small subset of the twitter network. Users are represented as nodes (cirlces) while the edges are defined by the follower property, which is native to twitter.

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In this figure several changes to the topology have occurred, some existing links have disappeared (red), but at the same time new links have emerged (green).

In order to study the dynamics of social networks, we have monitored 1 000 twitter users and their connections over a period of 30 days. For each of these days we captured a “snapshot” of the network topology at a given moment, and thus produced a series of 30 graphs each corresponding to a single day.

Using the temporal network we have obtained by monitoring twitter users we analyze its properties. First, we treat the temporal network as a series of independent graphs. This enables us to compute some standard metrics on each graph, and then see how each particular metric changes with time.

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Total number of links in the network.

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Maximum degree of the network, i.e. the maximum number of followers that a single user has. This continually increase with time, possibly indicating that the network has not yet converged.

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Clustering coefficient, which is continually decreasing, thus indicating that the network is moving away from a structure that consists of small groups of interconnected users to a more spread out topology.

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Bottom right is the average path length of the network which is decreasing with time. This can be interpreted as a natural tendency to increase the efficiency of information dissemination in the network.

Standard network metrics can provide some information about the social networks, but in order to truly understand them we need metrics that take into account the dynamic nature of the network. Thus we are focused on developing novel metrics that can help us study temporal networks. These types of metrics revolve around the concept of “journey” which is the temporal generalization of path in standard graphs.

By examining the properties of social networks, we aim to better understand the underlying processes that shape them. This knowledge can then be used to help improve the quality of social networking services or increase the effectiveness of a marketing campaigns on Twitter. We can also predict when a user is likely to unfollow a company’s news feed, or which individual he\she will follow next.