As for semisupervised learning, both label information and side information serve as pivotal indicators for the classification. Nonetheless, most of related research works utilize either label information or side information instead of exploiting both of them simultaneously. To address the referred defect, we propose a graph-based semisupervised learning (GSL) problem according to both given label information and side information. To solve the GSL problem efficiently, two novel self-weighted strategies are proposed based on solving associated equivalent counterparts of a GSL problem, which can be widely applied to a spectrum of biobjective optimizations. Different from a conventional technique to amalgamate must-link and cannot-link into a single similarity for convenient optimization, we derive a new parameter-free similarity, upon which intrinsic graph and penalty graph can be separately developed. Consequently, a novel semisupervised classification algorithm can be summarized correspondingly with a theoretical analysis.