$\Phi$-harmonic functions on graphs

We study certain problems of $\Phi$-harmonic analysis on graphs, where $\Phi$ is a strictly convex $N$-function.We introduce the key definitions and reveal that the ones in question are well-defined and what basic properties of harmonic functions hold. Also we prove discrete analogs of classical theorems for harmonic function in the usual sense: uniqueness theorem, Harnack’s inequality, Harnack’s principle etc.