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Dear friends i searched alot to solve this problem.but no one has given proper answer. after trying one hour i found two problems
one is in user relationships they have given wrong variable name
at 72 line change $relationship to $rtype means
$css_class = array(str_replace(' ', '-', $relationship->name) change to $css_class = array(str_replace(' ', '-', $rtype->name)
and in authorpane module in author-pane.tpl.php file change at replace $user_relationships_api with $user_relationships
then it will work fine.thanks to michelle for great module