A multiplex network is a network model composed of a multiplicity of overlapping networks that capture the different types of connections between nodes within the network. When analyzing a large system like a metropolitan economy, a corporation or the global commodities market, what we are dealing with is a network that is embedded within many other networks. A metropolitan area will be a complex system where economic interactions are embedded within socio-political networks, transportation and geospatial networks and financial networks, in order to capture all of these overlapping networks it is optimal to use a multiplex network model. In a multiplex network, each type of interaction between the nodes is described by a single layer network and the different layers of networks describe the different modes of interaction. With a multiplex network, we can try and capture how these different connections interact and affect each other. This is a much more realistic picture that lies behind many phenomena and a lot more faithful to one of the basic premises of complexity theory, that is that many phenomena are in fact the product of a multiplicity of nonlinear interacting forces. As an example, we might think about the recent uprisings in Egypt. When we first look at this phenomenon we would consider it political in nature and start analyzing the political network, but research has shown a robust correlation between spikes in the price of basic foods and the occurrence of these riots, thus these events are an emergent phenomenon of different interacting networks, social, political and economic all putting stress on the social system. In this situation, it would be of use to use a multiplex network to try and model the overall dynamic. Phenomena like this are very complex they are embedded within many different overlapping networks, simply modeling one of these networks can only ever give a partial insight, thus a full representation necessitates multiplex network modeling.
1. Lee, K.-M., Min, B. and Goh, K.-I. (2015). Towards real-world complexity: an introduction to multiplex networks. The European Physical Journal B, [online] 88(2). Available at: https://epjqt.epj.org/images/stories/news/2015/10.1140--epjb--e2015-50742-1.pdf [Accessed 4 Sep. 2020].