Interest communities and flow roles in directed networks: the Twitter network of the UK riots

Abstract

Directionality is a crucial ingredient in many complex networks in which information, energy or influence are transmitted. In such directed networks, analysing flows (and not only the strength of connections) is crucial to reveal important features of the network that might go undetected if the orientation of connections is ignored. We showcase here a flow-based approach for community detection through the study of the network of the most influential Twitter users during the 2011 riots in England. Firstly, we use directed Markov Stability to extract descriptions of the network at different levels of coarseness in terms of interest communities, i.e. groups of nodes within which flows of information are contained and reinforced. Such interest communities reveal user groupings according to location, profession, employer and topic. The study of flows also allows us to generate an interest distance, which affords a personalized view of the attention in the network as viewed from the vantage point of any given user. Secondly, we analyse the profiles of incoming and outgoing long-range flows with a combined approach of role-based similarity and the novel relaxed minimum spanning tree algorithm to reveal that the users in the network can be classified into five roles. These flow roles go beyond the standard leader/follower dichotomy and differ from classifications based on regular/structural equivalence. We then show that the interest communities fall into distinct informational organigrams characterized by a different mix of user roles reflecting the quality of dialogue within them. Our generic framework can be used to provide insight into how flows are generated, distributed, preserved and consumed in directed networks.

Keywords: Twitter; UK riots; community detection; directed networks; flow roles; graph theory and stochastic processes.

Figure 1.

Interest communities at all scales as detected by Markov Stability. (a) The number of communities at each Markov time (t). The inset shows the network with nodes and edges coloured according to their community at four illustrative Markov times. Two of these partitions at different resolutions are shown in more detail. (b) At relatively short Markov times (t_I = 0.15), we find 149 communities (coarse-grained network view in the centre). Three examples of communities in this partition are ‘police and crime reporting’ (top), ‘Hackney’ (bottom), ‘the Daily Telegraph’ (left) shown with their members and their self-description word clouds. (c) At longer Markov times (t_IV = 7) we find four communities (coarse-grained view in the centre): three large communities broadly corresponding to ‘UK’ (bottom-right), ‘international’ (top), ‘celebrities/entertainment’ (bottom-left) and a small one corresponding to the ‘BBC’ (right). A detailed view of the partitions can be found in the electronic supplementary material.

Figure 2.

Communities containing the account of BBC Radio 4's Today programme (bbcr4today) in the undirected (top, diamonds) and directed (bottom, circles) versions of the network at Markov times t = 0.86, t = 1.3 and t = 7.0, along with their word clouds. In the middle we show the size of the communities of the Today programme in both versions of the network for Markov times between 10⁻¹ and 10¹. (Online version in colour.)

Figure 3.

Directed and undirected communities containing the account of George Monbiot (georgemonbiot) obtained from the undirected (top, diamonds) and directed (bottom, circles) networks at Markov times t = 0.8603, t = 1.3049 and t = 7.0, along with their word clouds. Compare these results with those obtained in figure 2 for BBC Radio 4's Today programme. (Online version in colour.)

Figure 4.

(a) Personalized view of the network from the vantage point of ‘Anonymous’ based on interest distance. The interest distance (gradient from red to blue, or dark to light in black and white) is defined as the earliest Markov time at which a node belongs in the same interest community as ‘Anonymous’. The number of users in the interest community of ‘Anonymous’ (represented by the width of the line) grows as the Markov time increases, as users join the community at different times. We show the top 10 users (according to PageRank) of every batch that joins the Anonymous community. (b) The reverse personalized views from two vantage points that are of least interest to ‘Anonymous’: (i) from the vantage point corresponding to Wayne Rooney and several footballers and (ii) from the vantage point of actor Stephen Fry. (Online version in colour.)

Figure 5.

Flow-based roles in the Twitter network. (a) Role similarity graph obtained from the path similarity matrix using the RMST algorithm. The size of the nodes is proportional to the in-degree in the Twitter network. Nodes with similar profiles of in- and out-paths of all lengths in the original Twitter network are close in this role similarity graph. The role similarity graph is found to contain five robust clusters, corresponding to flow roles (see Methods and electronic supplementary material). (b) The original Twitter network coarse-grained according to roles, with arrows proportional to users in one role class who follow users in another role class. (c) Pattern of incoming and outgoing interest at all path lengths: (left) nodes in red (dark) receive the most attention with higher numbers of incoming paths, while nodes in blue (light) receive the least amount of attention; (right) nodes in red pay the most attention with higher numbers of outgoing paths, while nodes in blue pay the least amount of attention with few outgoing paths. (d) Cumulative distribution of retweets for each of the five roles: highly retweeted nodes are heavily present in the references and engaged leader categories (longer tails) and mostly absent in both listener categories. The mediator category lies in between.

Figure 6.

Mix of roles of the 15 interest communities found at t = 1.3. The communities reflect a diverse set of topical groupings (see word clouds with the top 50 non-trivial words in the user biographies) and are characterized by different mixes of the five flow roles, as shown by the pie charts. The organigrams range from reference-listener schemes (‘broadcast’ and ‘monologue’) to more balanced dialogue communities (‘engaged dialogue’ and ‘dialogue in public’) in which engaged leaders, mediators and diversified listeners dominate.