We study the structure of a social network of strong ties (trust network) investigating its property of connectedness versus fragmentation. To this purpose we analyse an extensive set of census data, about marrying or having children with immigrants, collected by Italian national statistical institute for all Italian municipalities from 2001 to 2011. Not using neither obtaining personal local information but only average ones, our method fully complies with privacy and confidentiality. Our findings show that large cities display the behaviour of highly fragmented trust networks where individuals face possible phenomena of alienation. Smaller cities and villages instead behave like fully connected social systems with a rich tie structure, where isolation is rare or completely absent. While confirming classical sociological theories on alienation in large urban areas our approach provides a quantitative method to test them and a predictive tool for policy makers.