**4. Conclusions**

A network science-based analytical approach is proposed for the structural analysis of heat exchanger networks.

The proposed methodology utilises three different network-based representations that highlight various aspects of the dynamics of the HEN. The extracted networks were analysed by the toolbox of network science to create structural operability and complexity measures.

The analysis of more than 600 HENs confirmed that the proposed approach can be efficiently applied to the fast screening of HENs based on their structural properties.

A significant result of the analysis is that the popular maximum matching-based method used to determine the sensor and driver nodes in dynamical systems was not suitable for heat exchanger networks due to the intrinsic dynamics. It was highlighted that, with the more interconnected the HENs, fewer actuators and sensors are needed to ensure structural controllability and observability, which results in a higher relative order and the increased difficulty of the operability.

It was also highlighted that the degree-based structural measures can refer to the level of Heat Integration. The methodology was suitable for classifying the different methods that gran<sup>t</sup> the HEN, as some techniques tended to determine more units in the network than others.

Although the proposed methodology has been introduced for the analysis of HENs, it can be applied to a broader class of dynamical systems. In our further research, we will generalise the results by examining the integrated and multi-objective design of processes and their control systems and studying the network topology-based properties of dynamical systems.

**Author Contributions:** D.L. reviewed the literature on network science and heat exchanger networks, developed the algorithms, designed and performed the experiments, and wrote the related sections. A.V.-F. participated in the formalisation of the methodology. J.A. conceived and designed the core concept, developed the algorithms and proofread the paper.

**Funding:** This research was supported by the National Research, Development and Innovation Office NKFIH, through the project OTKA-116674 (Process mining and deep learning in the natural sciences and process development) and the EFOP-3.6.1- 16-2016- 00015 Smart Specialization Strategy (S3) Comprehensive Institutional Development Program. Daniel Leitold was supported by the ÚNKP-18-3 New National Excellence Program of the Ministry of Human Capacities.

**Conflicts of Interest:** The authors declare no conflicts of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.
