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Google Inc.’s social network debuted at the top spot on a customer-service index of social-media websites, including Facebook Inc., which sank to a record low in the annual report.

Google+, which was started in June 2011, tied information aggregator Wikipedia with a score of 78 in the social-media category on the American Customer Satisfaction Index E-Business Report, which ranks companies on a 100-point scale. Facebook, criticized for changes to its interface, had a score of 61, down from 66 last year and 64 in the 2010 report.

Already owner of the world’s largest search engine, Google is counting on Google+ to help it challenge Facebook for user attention and to provide more data to improve its core web-query service. Google+ already has reached more than 250 million users, compared with more than 900 million for Facebook.

“Facebook is having a hard time with its customers, but they kind of own the concept of social network,” said Larry Freed, chief executive officer of researcher ForeSee Results Inc., which helps produce the index for the Internet industry. “If you want to see pictures of your grandkids or share them with your grandparents, you’re not going to find them on Google+ today. But if that network continues to grow, then they could be a very serious competitor.”

As a category, social media slipped 1.4 percent in the customer-satisfaction index to 69, the ACSI said. Twitter Inc., the microblogging service that has more than 140 million users, was a new entry to the category with a score of 64.

LinkedIn, Pinterest

Professional-networking site LinkedIn Corp. had a score of 63, and Pinterest Inc., an image-based social site, fared better at 69. Both were also new entries to the category.

Facebook’s score of 61 puts it among the five lowest-scoring companies of the 230 that the ACSI measures across different markets. Other complaints about Facebook included an excess of ads and privacy concerns, Freed said.

The ACSI was founded at the University of Michigan’s Stephen M. Ross School of Business in Ann Arbor. To compile the index, data from interviews with about 70,000 customers annually are used to help measure satisfaction on the companies, which include 47 industries and 10 economic sectors.