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Let $G$ be a connected $m$-uniform hypergraph. In this paper we mainlyconsider the eigenvectors of the Laplacian or signless Laplacian tensor of $G$associated with zero eigenvalue, called the first Laplacian or signlessLaplacian eigenvectors of $G$. By means of the incidence matrix of $G$, thenumber of first Laplacian or signless Laplaican (H- or N-)eigenvectors can beget explicitly by solving the Smith normal form of the incidence matrix over$\mathbb{Z}_m$ or $\mathbb{Z}_2$. Consequently, we prove that the number offirst Laplacian (H-)eigenvectors is equal to the number of first signlessLaplacian (H-)eigenvectors when zero is an (H-)eigenvalue of the signlessLaplacian tensor. We establish a connection between first Laplacian (signlessLaplacian) H-eigenvectors and the even (odd) bipartitions of $G$.

Eigenvectors of Laplacian or signless Laplacian of Hypergraphs Associated with Zero Eigenvalue