Degree (k)

Transcription

1 0 1 Pr(X k) Degree (k) Figure A1: Log-log plot of the complementary cumulative distribution function (CCDF) of the degree distribution for a sample month (January 0) network is shown (blue), along with the best fitting power law model ( =. and k min = ) using the procedure of Clauset, Shalizi, and Newman []. We test whether the empirical distribution is distinguishable from a power law using the Kolmogorov-Smirnov test and find no evidence against the null hypothesis (D = 1., p = 0., n = 1) data. This distribution may be fit by a power law. Assortativity Week Spearman Pearson Figure A: Spearman and Pearson correlation coe cients are used to measure degree assortativity. The Pearson correlation coe cient is more sensitive to extreme values. As a result, the Pearson correlation coe cient obscures the trend that the network is assortative with respect to the rank of node degrees. Given the nature of the degree distribution and the questions that we are asking, we use the Spearman correlation coe cient for our study.

2 0 1 r p r s Threshold (α) (a) Assortativity of happiness, Pearson s r Threshold (α) (b) Assortativity of happiness, Spearman s r Δ h=0 Δ h=0. Δ h=1 Δ h=1. Δ h= Δ h=0 Δ h=0. Δ h=1 Δ h=1. Δ h= Figure A: Measured happiness assortativity as threshold for labmt word usage increases for a single week network. The Spearman correlation coe cient (right) exhibits less variability as compared to the Pearson correlation coe cient (left). Notice that when h = 0, there is less variation due to the numerous words centered around the mean happiness score, regardless of the threshold,.

3 0 1 Figure A: A visualization of the reciprocal reply network for the week beginning September, 0 (Week 1) is depicted. The size of a node is proportional to the degree, and colors further emphasize the degree detected by Gephis implementation of the algorithm suggested by Blondel et al. [].

4 0 1 Figure A: A visualization of the reciprocal reply network for the week beginning September, 0 (Week 1). Colors represent happiness scores for nodes with greater than = labmt words (% of all nodes in the week). The visualization was produced using Gephi []. The algorithm employed by the software clusters nodes according to their connectivity. Collections of nodes with similar colors provide a visualization of the happiness is assortativity finding.

5 0 1 Figure A: A visualization of the reciprocal reply network for the day of October, 0. The size of the nodes is proportional to the degree and colors indicate communities detected by Gephi s implementation of the community detection algorithm suggested by []..

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8 0 1 Rank Word Frequency Happiness Rank Word Frequency Happiness Rank Word Frequency Happiness ( ) ( ) ( ) 1 you.. sure.. 1 music..0 my.1. done.1. found.. me.. show.. doesn t.. not.. awesome.. online.. up.0. check.. party.. no.. bed.. soon.. new.0. sleep.. thinking.. like 1.. cool.. snow.. all 0.1. live.. give.. good 0.. big.. 1 movie.. will..0 free.. 1 ha.0.00 we.. life.. 1 sorry.0. day.0. old.0. 1 real.0. know.. didn t kids.. more.. find phone.1. don t..0 die tv.1.0 today.. video.. stop..0 love.. house.. play.. think.. christmas.. 1 waiting.. see..0 0 playing.. 1 lunch.1. great.. 1 world.. 1 food.. lol.. game.. 1 reading.. thanks.0. wow.. god.. home.0. ready.. top.. people.1. iphone.. buy.. night.0. listening.. book.. blog..0 pretty.. car.. last.. always.. idea..0 well.0. help..0 friend.. 0 make read.0. 0 family.. 1 right.0. 1 google.0. 1 yay.. can t.. everyone.0. glad.. morning.. most.. least..00 very.. wait.. nothing..0 first.. start.. late.. our..0 please.. internet.. better..00 con..0 amazing.. us.. try..0 mean.. tonight.. thought.. myself..0 down.. 0 school.. 0 facebook..0 happy..0 1 thank.. 1 funny.. tomorrow.. weekend..00 tired.. nice.0. hey..0 talk..0 best.. wish.. damn.. she.. hate.. interesting.. yes.. haha.. own.. fun.. friends.. friday.. hope.. making.. open.. bad.. dinner.. lost.. never.. 0 co ee.. 0 guys.. Table A1: The top 0 most frequently occurring words from the labmt list in our Sept 0 through Feb 0 data set, where stop words ( < h avg < ) have been removed.

9 0 1 Rank Word Frequency Happiness Rank Word Frequency Happiness Rank Word Frequency Happiness ( ) ( ) ( ) 1 the.. an.. 1 el..0 to.1. we.. well.0. i 1.. some..0 oh.. a.. que.. who..0 and.. day.0. should.. is.. how.. over.. in 1.. going.. make..00 of 1.. am.. then.. for 1.. go.0. right.0. you.. has.. 1 can t.. on.. or.. 1 way.. my.1. know.. 1 only.. it more.. 1 getting.. that.1. la his.. at..0 don t..0 1 morning.. with.. today.. 1 very.. me.. too.. after..0 just.. they.0. watching.. have.. work.. 1 her.. be.. 0 got.1. 1 them.1. this..0 1 love.. 1 first.. de.. think.. 1 e.. so..0 back.. that s.. not.. twitter.. rt.. i m.. when.. y.. are.0. there.. than.. but.. had.0. its.. was.. see..0 our..0 up.0. en.. better out.. 0 really.. 0 us.. 1 now..0 1 o..0 1 tonight.. no.. great.. down.. new.0. need.. i ve.. do.. he.. u.. from.. still.. happy..0 like 1.. been..0 again.. your 1.. lol.. could.. all 0.1. would.. un.. good 0.. thanks.0. into.0.0 get home.0. 0 i ll.0. what..0 1 want man..0 about.. people.1. tomorrow.. it s.. night.0. nice.0. if.. here.. any.0. by.. o.. take.. as.. blog..0 best.. time.. why.. she.. one.. much.. even.. will..0 last.. yes.. can.. 0 did.. 0 little.. Table A: The top 0 most frequently occurring words from the labmt word list in our Sept 0 through Feb 0 data set including stop words.

10 0 1 Week Start date N < k > k max C G Assort # Comp. S Table A: Network statistics for reciprocal-reply networks by week. As Twitter popularity grows, so does the number of users (N) in the observed reciprocal-reply network. The average degree (< k >), degree assortativity, the number of nodes in the giant component (# Comp.), and the proportion of nodes in the giant component (S ) remain fairly constant, whereas the maximum degree (k max ) shows a great deal of variability from month to month. Clustering (C G ) shows a slight decrease over the course of this period.

11 0 1 Week Start date # Obsvd. Msgs. # Total Msgs. % Obsvd. # Replies % Replies #Obsvd. #Total 0 #Replies #Obsvd Table A: The number of observed messages in our database comprise a fraction of the total number of Twitter message made during period of this study (September 0 through February 0). While our feed from the Twitter API remains fairly constant, the total # of tweets grows, thus reducing the % of all tweets observed in our database. We calculate the total # of messages as the di erence between the last message id and the first message id that we observe for a given month. This provides a reasonable estimation of the number of tweets made per month as message ids were assigned (by Twitter) sequentially during the time period of this study. We also report the number observed messages that are replies to specific messages and the percentage of our observed messages which constitute replies.