Summary: In order to investigate the non-odd-bipartiteness of even uniform hypergraphs, starting from a simple graph \(G\), we construct a generalized power of \(G\), denoted by \(G^{k, s}\), which is obtained from \(G\) by blowing up each vertex into a \(s\)-set and each edge into a \((k - 2 s)\)-set, where \(s \leq k / 2\). When \(s < k / 2\), \(G^{k, s}\) is always odd-bipartite. We show that \(G^{k, \frac{k}{2}}\) is non-odd-bipartite if and only if \(G\) is non-bipartite, and find that \(G^{k, \frac{k}{2}}\) has the same adjacency (respectively, signless Laplacian) spectral radius as \(G\). So the results involving the adjacency or signless Laplacian spectral radius of a simple graph \(G\) hold for \(G^{k, \frac{k}{2}}\). In particular, we characterize the unique graph with minimum adjacency or signless Laplacian spectral radius among all non-odd-bipartite hypergraphs \(G^{k, \frac{k}{2}}\) of fixed order, and prove that \(\sqrt{2 + \sqrt{5}}\) is the smallest limit point of the non-odd-bipartite hypergraphs \(G^{k, \frac{k}{2}}\). In addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors.