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Correctly ascertaining the factor structure associated with data obtained from an instrument is a crucial piece of evidence for establishing construct validity, an essential consideration in assessment. Using exploratory graph analysis (EGA) to estimate factor structure may outperform alternatives when the underlying structure is complex. This study investigates how EGA-estimated factor structures are affected by changes in intercorrelation among factors and the degree of cross-loading of items. Data (n=500) were simulated for ten conditions. In nine of ten conditions, EGA correctly identified the underlying structure, but incorrectly identified the structure of the condition with the greatest factor correlation (0.50) and cross-loadings (0.30). EGA shows promise for identifying dimensionality in scale data to assist in establishing construct validity.