An updated a list of City of Edinburgh Councillors (post 2012 elections) who have Twitter accounts (not all are "active"), but are as far as I can tell, are genuine. I am also on Twitter @kim_harding.
CouncillorPolitical PartyTwitter address
Elaine AitkenConservativeN/A
Ewan AitkenLabour@EwanAitken
Robert C AldridgeLib-DemN/A
Jeremy R BalfourConservativeN/A
Eric BarryLabourN/A
Angela BlacklockLabourN/A
Mike BridgmanSNPN/A
Deidre BrockSNP@DeidreBrock
Gordon BuchanConservativeN/A
Tom BuchananSNP@tombbuchanan
Steve BurgessGreen@SteveAMBurgess
Andrew BurnsLabourAndrew Burns
Ronald CairnsSNPN/A
Steve CardownieSNPN/A
Maggie ChapmanGreen@MaggieEdinburgh
Maureen M ChildLabour@MaureenChild1
Joanna ColemanLib-Dem@Joanna_Coleman
Bill CookLabourN/A
Jennifer A DaweLib-DemN/A
Cammy DayLabour@cllrcammyday
Charles DundasLib-Dem@cdundas
Paul G EdieLib-Dem@paul_edie
Nick Elliott-CannonSNPN/A
Paul GodzikLabour@PaulGodzik
George GrubbLib-DemN/A
Norma HartLabour@normamayhart
Stephen HawkinsLib-DemN/A
Ricky HendersonLabour@henderson_ricky
Lesley HindsLabour@LAHinds
Allan G JacksonConservativeN/A
Alison JohnstoneGreen@AlisonJohnstone
Colin KeirSNPN/A
Louise LangLib-Dem@CllrLouiseLang
Jim LowrieLib-DemN/A
Gordon MackenzieLib-DemN/A
Kate MacKenzieConservativeN/A
Marilyne A MacLarenLib-DemN/A
Mark McInnesConservative@Morningsidemark
Stuart Roy McIvorSNPN/A
Tim McKayLib-DemN/A
Eric MilliganLabourN/A
Elaine MorrisSNPN/A
Joanna MowatConservative@jomowat
Rob MunnSNP@robm2
Gordon J MunroLabourN/A
Alastair PaisleyConservativeN/A
Gary PeacockLib-DemN/A
Ian PerryLabourN/A
Alasdair RankinSNPN/A
Cameron RoseConservative@cameronrose
Jason G RustConservativeN/A
Conor SnowdenLib-Dem@DrSnowden
Marjorie ThomasLib-DemN/A
Stefan TymkewyczSNP@tymkewycz
Phil WheelerLib-DemN/A
Iain WhyteConservativeN/A
Donald WilsonLabourN/A
Norrie WorkSNPN/A

If you spot any errors, please let me know, I am also on Twitter @kim_harding.

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