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NEW YORK — What began as a tepid courtship between fashion and social media has become an all-consuming love affair as designers unveil new digital initiatives for fashion week.

“Ignoring the 

Internet is total madness,” said Diane von Furstenberg, who didn’t live stream her show Sunday but did update her Facebook page with backstage photos and tweeted from the event. “Being active on the Internet is indispensable to growth and for being relevant. It helps your business to be truly global and truly multigenerational.”