Network embedding aims to represent nodes with low dimensional vectors while preserving structural information. It has been recently shown that many popular network embedding methods can be transformed into matrix factorization problems. In this paper, we propose the unifying framework “Z-NetMF,” which generalizes random walk samplers to Z-Laplacian graph filters, leading to embedding algorithms with interpretable parameters. In particular, by controlling biases in the time domain, we propose the Z-NetMF-t algorithm, making it possible to scale contributions of random walks of different length. Inspired by node2vec, we design the Z-NetMF-g algorithm, capturing the random walk biases in the graph domain. Moreover, we evaluate the effect of the bias parameters based on node classification and link prediction tasks. The results show that our algorithms, especially the combined model Z-NetMF-gt with biases in both domains, outperform the state-of-art methods while providing interpretable insights at the same time. Finally, we discuss future directions of the Z-NetMF framework.