Table 2.

Most important channels in the main downstream, core and upstream clusters for the network $G_1$ in Fig. 4 corresponding to the period Sep. 2015 to June 2019

Size rank	Top channels in downstream communities
1 ($D_R$)	kremlin_mother_expert, sexy_moscow, solarstorm, TJournal, gorod095, nebrexnya, justthejudge, nourlnews, varlamov, pro_IT_2018
2 ($D_F$)	realdonaldtrump, WhiteHouse, breaking911, jahan_24, POTUS, ancapistantm, ReutersWorldChannel, YLYL4chan, dailyredpill, XDProductions, DieForIsraelGoy, AnarchoMemes, AltMemes, khamenei_ir, anarchiaautonomia, animach, PoliticalMemes, DanScavino, foxnews, roopab
4	Redes7, OlavoTemRazaoCanal, Noticias2018, ###, HA_alshami02, criticanacional, PatriotasConservadores, almubeen102, red_color, BrasilSurreal

Size rank	Top channels in core communities
3 ($C_R$)	go338, karaulny, kbrvdvkr, rt_russian, stormdaily, bbbreaking, kononenkome, operdrain, tv360ru, mediatech
6 ($C_F$)	randomanonch, Thecelticempire, WhiteIsRight, sgmeme, BloodAndHonour, NazBol, CIGtelegram, beadymanor, MiloOfficial, shitpost, toalibertarian, TommyRobinsonNews, pjwnews, pol_4chan, HansTerrorwave, officialmilo, loomeredofficial, AntifaPublicWatch, V_of_Europe*, JackDawkins
10	just_hmmm, r_unexpected, programmer_humor, get_happiness, awwnime, r_behindthegifs, PoliticalHumor, r_Showerthoughts, r_dankmemes, r_HighQualityGifs

Size rank	Top channels in upstream communities
12 ($U_R$)	severnygorod, live_kuban, vampov, ErnestMakarenko, gorodbratsk, ci_newsblock, na_rajone, ordynets, sevenandmedia, lubiczonline
13 ($U_F$)	LeHumbleKekVerse*, contraototalitarismodaonuenom, brexiteerschatlounge*, judenpresse_archive, q_anons*, CrypticCoinVIP*, fitinorfuckoff*, trrchat*, Onehundredfags*, KingdomZombe*, News_cabinet_news, bannedforlife, IB_MeckPomm, tehmoonwalkers*, thecarnalconservative, SundayLongLive*, childrenmatter*, letzcrowd, DieWahrheitnurdieWahrheit, ###

We give the top channels ranked by their in-Katz centrality for channels in the downstream and core clusters and ranked by their out-Katz centrality in the upstream clusters. We show the top 20 channels, sorted according to their Katz score, in communities linked to the UK and US far-right and the top 10 channels in other communities. Channels marked with an asterisk correspond to group chats while the other ones correspond to broadcast channels