  The syntax of modal graphs is defined in terms of the continuous cut and
broken cut following Charles Peirce's notation in the gamma part of his
graphical logic of existential graphs. Graphical calculi for normal modal
logics are developed based on a reformulation of the graphical calculus for
classical propositional logic. These graphical calculi are of the nature of
deep inference. The relationship between graphical calculi and sequent calculi
for modal logics is shown by translations between graphs and modal formulas.
