Anthropologists have observed that gifts bring goods to the recipient and honour to the donor in many human societies. The totality of such social relationships constitutes a network. Social networks characterise different types of social organisations including bands of small kin groups, tribal unions of families, and hierarchically organised chiefdoms. However, the factors and mechanisms that cause the transition between these types have hardly been explained. Here, we focus on gifts as the driving force for such changes. We build the model by idealising gift interactions and simulating the consequent social changes due to long-term massive interactions. In the model, people give their wealth to each other, produce wealth, and reciprocate for the gift. Gifts and reciprocation strengthen relationships. Through simulation, we demonstrate that, as the frequency and scale of gifts increase, economic and social disparities successively arise. Simultaneously, network structures shift from bands to tribes and then, chiefdoms. Statistical analysis using the Standard Cross-Cultural Sample, a global ethnographic database, empirically verifies the theoretical results. The constructive simulation study, as presented here, explains how people's interactions shape various social structures in response to environmental conditions. It provides the basic mechanistic explanation for social evolution and integrates microscopic and macroscopic theories in social sciences.