Although the horizontal expansion of cities is mentioned in the literature as one of the reasons for the decline and instability of the central core, this study intends to show, by using spatial analysis models, such as Getis-Ord Gi and Grouping Analysis, and the spatial diffusion approach, that this conclusion differs in small cities. The study area is Torqabeh City, located in the northeast of Iran with a population of 20,998. Since 2006 the city has experienced rapid physical expansion with an annual growth rate of 5.27%. The research variables were population number, number of women, elderly, young, employed, unemployed and illiterate. The analysis was performed on 1,476 urban blocks across 1996, 2006 and 2016. The results indicated that before 2006, the central core as a \\\\\\\"hot spot\\\\\\\" was the origin of all population groups and was distinct from other urban areas. However, after 2006, population groups with the dominant pattern of \\\\\\\"contagious diffusion\\\\\\\" left the central core and settled around it. The outcomes of these changes did not show signs of decline and instability of the central core of Torqabeh in response to rapid physical expansion. This may be due to the failure of the new areas to play the role of a destination for the spatial diffusion of population groups and the lack of change in the position of the central core from a \\\\\\\"hot spot\\\\\\\" to a \\\\\\\"cold spot\\\\\\\". On the other hand, the diffusion of population groups from the central core to the peripheral areas, connected to the core in Torqabeh City, caused these areas to be similar to the central core and indicated the different condition of this city when compared to central core changes in big cities.

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