Strategic energy flows in input-output relations: a temporal multilayer approach (Short Version)

Modern energy systems are increasingly vital for the delivery of various essential services. These services include clean water, sanitation, healthcare, reliable and efficient lighting, heating, cooking, mechanical power, transportation, and telecommunications. The adoption of modern energy systems has resulted in notable enhancements in the quality of life for a significant portion of the global population. Typically, an energy system encompasses a complex and comprehensive structure that considers various elements such as energy production, transformation, transport, and distribution. In recent times, a great importance has been devoted to energy security, which is essential for the well-being associated with energy. Energy security involves two main aspects: longterm investments to align energy supply with economic and environmental needs, and short-term focus on the energy system’s ability to respond swiftly to supply-demand shifts and maintain resilience. Furthermore, it is crucial to establish a strong connection between energy security and climate change mitigation initiatives. Indeed, as highlighted in [9], in order to maximize the effectiveness of their energy policy, nations must integrate considerations of energy security and climate change mitigation priorities concurrently. Countries should prioritize both to optimize their energy policies’ efficiency, as referenced in . Energy access also presents a significant issue of inequality, with uneven distribution of energy sources across the globe. This lack of equitable access to energy sources poses challenges for sustainable development (see [13], [14] and [7]). Several factors drive the evaluation of energy system resilience and guide policymakers towards sustainable policies. These include energy consumption, the transfer of direct and indirect energy resources through international trade, transitioning to renewable energies, and promoting environmental sustainability. In this context, it is common practice to focus solely on direct energy. However, it is important to recognize that the production of goods and services also involves indirect energy. This indirect energy, also known as embodied energy, refers to the energy consumed during the production of goods and services that is required to create the final product (see [2] and [15]). The literature extensively examines the concept of energy embodied in international trade ([12], [17] and [18]). Interdependencies between industries within the economy has been initially depicted by Leontief, showcasing how the output of one sector can serve as an input for another sector, as discussed in [10] and [11]. Building upon this foundation, an extended input-output analysis (EEIOA) has been developed to assess the environmental and social impact of economic activities, including the extraction and depletion of natural resources. This approach has been utilized in studying the interconnected and intricate flows of embodied energy in international trade from a network perspective. Numerous tools have been employed to examine direct energy commodity trade networks and explore the characteristics of embodied energy in trade at global, national, and regional levels, as seen in [3], [5], [8] and [19]. However, the conventional monoplex network representation used in the literature fails to capture the joint interaction between sectors and countries, as it primarily focuses on either country-level or sector-level analysis. To address this limitation, more recent approaches, such as the one presented in [4], have adopted a multilayer network framework to provide a more comprehensive understanding of this complex topic. In this work, we expand upon the approach presented in [4] by considering various types of embodied energy sources and incorporating the temporal evolution of interactions between sectors and countries. Specifically, we focus on analyzing the flow of embodied energy within temporal multilayer networks, differentiated by renewable and non-renewable sources. We build upon existing methodologies outlined in [3] and [4] by calculating the embodied energy flows for each combination of countries and sectors in each time period, taking into account different energy sources. For a given time and energy source, these flows are used to construct a directed and weighted multilayer network, where sectors/industries serve as nodes and each layer represents the economy/ country. The weighted arcs within each layer reflect the magnitude of directed embodied energy flows between different sectors within the same economy during a specific time period, based on either renewable or non-renewable sources. Similarly, the weighted inter-layer arcs represent directed flows between the same or different sectors in different countries. By combining the multilayer networks across time periods for the same energy sources (renewable or non-renewable), we can create a temporal multilayer network that captures both the interactions between sectors and countries and their evolution over time, with the aim of identifying critical sectors and economies within the system.