Both the KCL and KVL equations are required to completely model a resistor network. However, the two main methods to analyze these circuits Nodal analysis and Mesh analysis only use KCL and KVL respectfully. In other words,these methods don't use the "complete model of the circuit" (i.e. Nodal analysis ignores the KVL part of the circuit model). Yet somehow they're able to completely analyze the entire circuit - how? How is something that doesn't take the entire model into account able to completely analyze the circuit?