Abstract The proliferation of network research has confused the meaning of the concept of network. To enhance conceptual clarity, this paper distinguishes between four concepts of network: economic, social, socio-economic, and objectual. Each of these has a different understanding of the fundamental character of networks. They also differ in relation to methodological choices, understanding of the historicity of networks as well as trust and sociality within networks. Each of the concepts also regards different things as essential: in the economic concept, this is oscillation between market and hierarchy; in social, embeddedness of economic activity in non-economic sociality; in socio-economic, sociality and trust within economic activity;...