Local and urban squares play a crucial role in the presence and participation of people and in their interaction promotion. Alexander explained the profound geometric relations and discipline in nature, using the concept of life phenomenon theory and living structures. He believes that humans can revive creatures through creating strong centers and an integrated whole. This study selects Avicenna tomb square and center of Aqajani Beig neighborhood, Hamedan. The main research questions include what the role of Alexander’s theory of living centers is in promoting the social interaction in local and urban square and which pattern of Alexander’s theory mostly affects social interactions in squares and how the individual factors impact social interactions in local and urban squares. Results reveals that patterns of Alexander’s theory are efficient in promoting social interactions in local and urban squares. Individual factors are not effective in this regard, but strong centers and urban square contradictions are more effective in resident’s social interactions than that of void spaces and strong centers. Architects, planners, and urban designers can apply the results in designing new urban and local squares.