The four arrested may face defamation charges, which under the new regulations are levelled against those whose posts are deemed to be rumours and are viewed by more than 5,000 users or re-tweeted more than 500 times.
Defamation charges can lead to up to three years in prison or loss of political rights.
These people used social network services to fabricate and spread rumours, or forward rumors published on foreign websites, according to police.
China this week ordered netizens to give their real names during registration, in an apparent bid to take control of the unprecedented growth of instant messaging services in the Communist nation which has the world's largest number of Internet users.
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According to State Internet Information Office, the regulation aims at promoting a healthy development of the fast-growing instant messaging sector and safeguarding national security and public interests.
But police have detained or warned another 81 people for similar but slighter offences, state-run Xinhua news agency reported today.
Under the new rules users of instant messaging services are required to use their real names while registering.
The new rules were aimed at holding users responsible for content they put out in their accounts.