  The electronic states and topological properties of the biphenylene network
(BPN) are analyzed using a tight-binding model based on the $\pi$-electron
network. It is shown that tuning the hopping parameters induces topological
phase transitions, leading to the emergence of edge states owing to the
nontrivial topological Zak phase of the bulk BPN. Elementary band analysis
clearly gives the number of edge states, which are associated with the location
of Wannier centers. In addition, we have presented the conditions for the
emergence of corner states owing to the higher-order topological nature of BPN.
