Fig 1.
Schematic representation of the bipartite graph construction from raw data and of the projections on the semantic and interest mono-partite graphs.
Fig 2.
Stength, degree correlation and rich club index distribution for the two network projections.
Plot A and D: Strength distribution of the semantic (A) and users’ interest network (D). The distributions follow a power law with exponents respectively γ = -1.6 and γ = -1 respectively. In the case of the users’ interest graph a pronounced exponential tail is observed. Plot B and E: Degree correlation of the semantic (B) and users’ interest network (E). For the semantic graph the average neighbours' degree decreases sub-linearly with the degree. The decrease is faster for hubs. For the users’ graph the average neighbors’ degree increases very slowly with the degree for k<103. For the hubs (k>103) we observe a sub-linear decrease. Plot C and F: Normalized rich club index as function of degree for the semantic (C) and the users’ interest network (F) For both networks the index is increasing with the degree indicating the existence of correlations in the tow networks. The decrease for large value is an effect of the networks finite sizes.
Fig 3.
Communities description of the semantic network.
The semantic network can be divided in 6 communities. Plot A: chord diagram representing the interactions among communities and their strengths. The grey bands represent links among communities member and their width is proportional to the number of connections between the two. Plot B: the permanence time of hashtags in the communities. The red histograms indicate the fraction of hashtags entering the community, for the first time, at a specific time; the green one the leaving time. The shaded area corresponds to the average permanence time of the community contents. Plot C: steamgraph showing the relative activity of the communitiesat time t. The relative importance of the community at time t is evaluated as the number of tweets contacting at least one of the community ahshtags normalized tot toal number of tweets collectd at time t. For each day, the height of the band corresponds to the proportion of activity of each community (number of tweets) normalized to the total activity. The color code is the same as in plot A and each band in the stream graph corresponds to a specific community (C1 in the bottom,C6 on top).
Fig 4.
Robustness of the two mono projections of the network as a function of the removal of nodes (target strategy).
On the y-axes the size of the largest connected part of the network normalized to the size of the network, on the x-axis the fraction of nodes removed. On the left semantic network, on the right users interest one. The colored lines correspond to the results relative to the original networks. The black lines correspond to cases when network has been re-shuffled using ab-initio (dashed line) and the topological method (star-lined). The results are averaged on 100 replicas of the attack model and, for the rewired networks, for 50 replicas of the reshuffling process.
Fig 5.
Time series for the Jaccard index for the two networks: semantic on the left, users’ interest on the right.
For each of the three phases(Initial, Middle and Final) we have estimated the interpolating lines using Theil-Sen regression and the shaded area correspond on the 95% Confidence Interval. Figures A and C: dots represent the values of the Jaccard index for the Nodes at time t and at time t-1. Figure B and D: dots and line represent the values of the Jaccard index between the set of edges of the at time t and at time t-1.
Fig 6.
Top hashtags in the three phases of the Occupy Wall Street Movement.
Each square corresponds to one specific period of movement and report the top most used hashtags in the period. The size of the square around each hashtag is proportional to the number of times it has been used.
Fig 7.
Evolution of the users’ participation to the semantic communities during Occupy Wall Street Movement.
On the left end we have the hashtags used in the communities in the first phase of the movement; on the right end we have the same at the end of the movement. Connecting lines represent the flows of users whose interests in the discussion have changed during the period of the movement as represented from the different types of hashtags they use (i.e. users using hashtags in community i at the beginning and in community j at the end).