Fig 1.
Time series for the cumulative sum of retweet and reply activities for four tweets authored by the Trump account after the 2016 presidential election.
The temporal axis is logarithmically spaced to show early-stage growth. Insets represent the cumulative ratio of Nretweets/Nreplies for the same time period. Vertical lines with H, D, W, M correspond to hour, day, week, and month intervals. Triangles indicate inflection points where the second derivative of retweet volume transitions from positive to negative (see Sec. 3.2 and Fig 6). The tweets examined here only provide some illustrative examples of how response activity time series behave. Direct links to tweets for panel (A): https://twitter.com/realDonaldTrump/status/914269704440737792, panel (B): https://twitter.com/realDonaldTrump/status/1128051913419837442, panel (C): https://twitter.com/realDonaldTrump/status/968468176639004672, and panel (D): https://twitter.com/realDonaldTrump/status/810996052241293312. Tweet screenshots were collected on May 28, 2020.
Fig 2.
Time series histogram of maximum activity counts for tweets posted from the Barack Obama (A–C) and Donald Trump (D–F) Twitter accounts.
Each bin represents a collection of tweets at their original author date along with their respective maximum observed activity count. Bins with less than 2 tweets are shown as grey dots. We include all tweet types (e.g., advertisements, promoted, etc.); see Section 2.1 for information on collection methods. We annotate Trump’s declaration of candidacy and the 2016 US general election with solid vertical grey bars. A marked decrease in Obama account activity is apparent immediately following the 2016 election. The region of outliers in the Trump time series immediately preceding the 2016 election has been determined to be largely reflective of promoted tweets which have abnormal circulation dynamics on the platform [69].
Fig 3.
Ternary histograms and Nretweets/Nreplies ratio time seriesfor the @BarackObama (A–D) and @realDonaldTrump (E–H) Twitter accounts. The ternary histograms (A–C and E–H) represent the count of retweet, favorite, and reply activities normalized by the sum of all activities. White regions indicate no observations over the given time period. See Fig 4 for examples of full time series for response activity for example tweets. Heatmap time series (D and H) consist of monthly bins representing the density of tweets with a given ratio value. Single observations (bin counts <2) are represented by grey points. The two dates annotated correspond to the date of Trump’s declaration of candidacy (2015–05–16) and the 2016 general election (2016–11–09). We show the tendency for Trump tweets to have ternary ratio values with a greater reply component—with pre-candidacy tweets having higher variability and pre-election tweets having a higher Nretweets/Nreplies ratio value. Post-election Obama tweets have ternary ratio values with more likes than other periods for both Obama and Trump.
Fig 4.
Ternary time series for three popular Trump tweets, selected to represent messages in approximately the upper 90th percentile, 50th percentile, and bottom 10th percentile of Nretweets/Nreplies ratios.
The time series represent observations from first activity observation to the final observation of the tweet. These ternary time series contrast the simple 2-dimensional ratio trajectories and illustrate example trajectories through the 3-dimensional ratio space. See S1 and S2 Figs for the distribution of ternary ratio values for Obama and Trump tweets over time. Each of these three tweets were authored on May 25, 2019. Direct links to tweets for panels (A–D) https://twitter.com/realDonaldTrump/status/1097116612279316480, panels (E–H) https://twitter.com/realDonaldTrump/status/1155657137076527104, and panels (I–L) https://twitter.com/realDonaldTrump/status/1159083364965654528. Screenshots were collected on May 28, 2020.
Fig 5.
Histogram of final observed ratios for tweets authored by @BarackObama and @realDonaldTrump accounts.
Observations left of the dashed vertical line correspond to tweets that are considered ratioed. The shift in the distribution corresponding to Trump’s account can be plainly seen—with the account producing more tweets that are ratioed than compared with Obama’s account. For both accounts, tweets shown here are restricted to those authored after Trump’s declaration of candidacy. Of 16,708 tweets included from the Trump account, 3,015 (18%) have a Nretweets/Nreplies value less than or equal to 0 and 13,693 (82%) have a score greater than 0. Of 1,786 tweets from the Obama account, 7 (<1% have Nretweets/Nreplies values ≤ 0 while 1,779 (>99%) have values >0. From the distribution of ratio values we see that ratioed tweets are outliers for the Obama account while the Trump account often gets ratioed and has a lower ratio value on average.
Fig 6.
Distribution of inflection points, the local maxima of instantaneous retweet volume, , where
.
A and E: Example cumulative retweet time series and inflection points (solid triangles) for Obama and Trump tweets. Histograms show the distribution of inflection points across all tweets binned by time periods before (B and F), during (C and G), and after (D and H) the 2016 US presidential election campaign. The January 1st 2009 to June 15th 2015 period for Trump (F) contains inflection point counts that are largely reflective of low initial activity and high(er) late activity (months or years later) leading to unusually high values for seconds to first inflection point (>108 seconds). For Obama’s and Trump’s time in office, tweets experience inflection points around 1-minute and 1-day after the tweet is authored—indicating characteristic time-scales of activity waning. Histogram bin widths are in effect logarithmically spaced over the displayed time span. This has the effect of providing a higher temporal resolution for shorter timer periods. Direct links for Obama tweet (A): https://twitter.com/BarackObama/status/693571153336496128 and Trump tweet (E): https://twitter.com/realDonaldTrump/status/1090729920760893441. Screenshots were collected on May 28, 2020.
Fig 7.
Complementary cumulative distribution function for inflection point timing.
Roughly 90% of Obama inflection points (A) took place before 105 seconds (∼ 1 day) for the period before the 2016 election cycle. For the period during and after the 2016 campaign season, both Obama and Trump tweets (B) receive 10% of inflection points after roughly 106 seconds (∼ 10 days) from the initial tweet.
Fig 8.
Rank divergence allotaxonograph [68] for 1-grams from Trump account tweets authored after Trump’s declaration of his candidacy on June 16, 2015.
“Ratioed” tweets are those where the proportion of retweets over replies is less than 1 (Nretweets/Nreplies < 1), non-ratioed tweets accumulated a ratio greater than 1 (Nretweets/Nreplies > 1). There is a notable class imbalance. The majority of tweets are non-ratioed, with a median value of ∼ 2. To generate the above figure we examined 3,313 ratioed tweets and 15,274 non-ratioed tweets. The 1-grams “Fake”, “News”, “Russia” and “NFL” are ranked higher in the ratioed corpus. For the non-ratioed corpus, the 1-grams “Jeb”, “Carolina”, and “Ted” are ranked higher. This illustrates the tendency of ratioed tweets from this period to contain more politically contentious 1-grams related to Trump scandals. Non-ratioed tweets from this period more often contain campaign related messages. In the main horizontal bar chart, the numbers next to the terms represent their rank in each corpus, while terms that appear in only one corpus are indicated with a rotated triangle. The smaller three vertical bars describe the balances between the ratioed and non-ratioed corpora: 77.1% of total counts occur in the non-ratioed corpus; we observe 90.3% of all 1-grams in the non-ratioed corpus; and 61.7% of 1-grams in the non-ratioed corpus are unique to that corpus.