During the last two decades, the use of network methodologies in archaeological studies of interaction has gradually emerged. In this paper I will explore the social significance of networks, advocating the explicit use of Marxist-inspired social theory to increase our understanding of the patterns recognized through graph-theory. Crucial in this will be the new concepts of Means, Relations and Modes of Interaction and the Gramscian notion of hegemony. I will illustrate the potential of this approach, through a case study based in MBA and LBA southern Italy, focused on the sharing of stylistic features in pottery from Apulia in a period when the region was one of the loci of interaction with Minoan/Mycenaean Greece. Local pottery networks show the existence of intense interaction since the early phases of the MBA, before the main period of contact with the Aegean world. It is argued that such networks were influenced by the growing Aegean presence in the region and the overall hegemony of this wide cultural component. Through the later phases of the Late Bronze Age the level of local interaction further increases, while at the same time Aegean-type pottery almost disappears, suggesting a less hegemonic role for Aegean groups involved and a re-balancing of interaction.