We analyze the time series data of number of districts or cities in India that are affected by COVID-19 from March 01, 2020 to April 17, 2020. We study the data in the framework of time series network data. The networks are defined by using the geodesic distances of the districts or cities specified by the latitude and longitude coordinates. We particularly restrict our analysis to all but districts in the north-eastern part of India. Unlike recent studies on the projection of the number of people infected with SARS-CoV-2 in the near future, in this note, the emphasis is on understanding the dynamics of the spread of the virus across the districts of India. We perform spectral and structural analysis of the model networks by considering several measures, notably the spectral radius, the algebraic connectivity, the average clustering coefficient, the average path length and the structure of the communities. Furthermore, we study the overall expansion properties given by the number of districts or cities before and after lockdown. These studies show that lockdown has a significant impact on the spread of SARS-CoV-2 in districts or cities over long distances. However, this impact is only observed after approximately two weeks of lockdown. We speculate that this happened due to the insufficient number of tests for COVID-19 before the lockdown which could not stop the movement of people infected with the virus but not detected, over long distances.