The passivity of Fe-Cr-Ni ternary alloys is considered in terms of a continuous network of -Cr-O-Cr-bridges in the oxide film (which also contains and Ni2+ ions) or in terms of a continuous network of -Ni-O-Ni-bridges in the oxide film (which also contains Fe3+ and Cr3+ ions). The structure of the oxide is represented by a mathematical graph, and graph theory is used to calculate the connectivity of the oxide. This approach shows that a continuous network of -Cr-O-Cr-bridges occurs when the cation fraction of Cr3+ ions in the oxide is 0.30 or greater. A continuous network of -Ni-O-Ni-bridges occurs when the cation fraction of Ni2+ ions in the oxide is 0.55 or greater. Experimental results taken from the literature support the -Cr-O-Cr-model. (c) 2007 The Electrochemical Society.