Most computational models of neurons assume temporally constant ion concentrations and zero extracellular potentials. This paradigm limits our ability to computationally investigate the impacts of changing ion concentrations and extracellular potentials on the dynamics of single cells and networks. We previously developed the first neuron model to include both intra- and extracellular ion concentrations and electrical potentials in a biophysically consistent manner and illustrated how this influenced the dynamics of the cell (Sætra et al. 2020, PLoS Comp Biol). However, the neuroscience community has lacked a framework for studying such dynamics at the network level without taking shortcuts at the expense of biophysical consistency. Therefore, we introduce the electrodiffusive network model, which predicts intra- and extracellular ion concentrations (Na+, K+, Cl-, and Ca2+), electrical potentials, and volume fractions in a 1D network of so-called units. Each unit represents a neuron and its immediate surroundings, including glia and extracellular space (ECS), and builds on our previously published electrodiffusive neuron-extracellular-glia (edNEG) model (Sætra et al. 2021, PLoS Comp Biol). The neurons and glial cells are equipped with ion-specific channels and homeostatic mechanisms such as ion pumps and cotransporters. Ions can move between units via the ECS or glial syncytium, driven by diffusion and electric drift. Neurons can communicate through chemical synapses, as well as ephaptic coupling. We demonstrate that these features lead to new, interesting behavior that conventional models do not capture. For instance, high ECS K+ concentrations resulting from hyperactive neurons can trigger spontaneous firing in neighboring cells.