Remove rel from next_post_link

You could hook the filter ‘next_post_link’. Your hook function is passed the output string from your next_post_link() function call. You can use basic string operations to alter it as needed. Whatever you return is directly echoed out to the user’s browser.

Thanks for help i have solved it as

function add_class_next_post_link($html){
    $html = str_replace('<a','<a class="prev"',$html);
    return $html;
}
add_filter('next_post_link','add_class_next_post_link',10,1);
function add_class_previous_post_link($html){
    $html = str_replace('<a','<a class="next"',$html);
    return $html;
}
add_filter('previous_post_link','add_class_previous_post_link',10,1);