Wrong polycentricity-right polycentricity?: Insights from an empirical study in Tehran metropolitan region, Iran

Research Hypotheses and Key Findings
This study addresses a notable research gap by moving beyond traditional single-dimensional approaches to measuring polycentricity. Our central hypothesis is that the assessment of polycentricity is not static but dynamically influenced by a complex interplay of three key factors: boundary types, the number of centers, and temporal trends. We sought to determine how these variables, both individually and in combination, affect the measured degree and interpretation of polycentricity within the Tehran city-region over a 20-year period (1996, 2006, and 2016).

Notable Findings and Interpretation
The data reveals several significant findings that challenge conventional single-framework approaches to polycentricity measurement.
The Influence of Boundaries
• Significant Effect: Our LMM analysis demonstrates that boundary types (TP, TMR, and FUAT) have a significant impact on the measured degree of polycentricity for a majority of the indicators. This confirms that the geographical definition of an urban region fundamentally shapes its perceived spatial structure.
• Monocentric vs. Polycentric: A key finding is the distinct difference between the Tehran Province (TP) boundary, which consistently points to a monocentric structure, and the Tehran Metropolitan Region (TMR) and Functional Urban Area of Tehran (FUAT) boundaries, which show more polycentric structures. This highlights the critical role of boundary delineation—using a more functionally-defined area (TMR, FUAT) captures the true polycentric nature of the region more accurately than a formal administrative boundary (TP).
The Influence of Centers
• Non-Significant Effect: Surprisingly, the number of centers considered in the analysis did not have a statistically significant effect on the measured degree of polycentricity across most indicators. This suggests that for the Tehran city-region, varying thresholds for what constitutes a "center" (e.g., considering all centers versus only the top-ranked ones) may not be a primary determinant of the overall polycentricity level. This finding indicates that the spatial relationships between centers, rather than just their quantity, are the more critical factor.
The Power of Interaction
• Dynamic Relationships: The most compelling finding is the presence of significant interaction effects between time, boundaries, and the number of centers. This means that the influence of a boundary type on polycentricity is not constant; it changes over time and is affected by the number of centers being considered.
• Triple Interaction: A significant triple interaction among time, boundary types, and the number of centers was observed in a subset of indicators. This demonstrates that the combined influence of these three factors jointly shapes the polycentricity of the urban system in a complex, dynamic manner.