# Quantitative Characterization of Complex Systems--An Information Theoretic Approach
## 6 Discussion and Conclusions  
The simulated case study considered in this paper considers complex networks. To examine the use the information theoretic approach, we mapped the similarity of a complex network to a general communication channel. A typical communication channel consists of a source that sends information, a channel that acts as a medium to transmit the information, and a destination that receives the transmitted information. In terms of complex networks, network nodes and actors behave as both source and destination, constantly transmitting and receiving information, whereas the edges connecting the nodes of a complex network act as the medium of information transfer. The application of the concepts from information theory helped in understanding, at a system and sub-system level, the interdependencies \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time-Step** & **Dynamic Entropy** & **R\({}_{0}\)** \\ \hline
0 & 3.906 & 0.014286 \\
1 & 3.894 & 0.014603 \\
2 & 3.894 & 0.014603 \\
3 & 3.888 & 0.014762 \\
4 & 3.882 & 0.014921 \\
5 & 3.888 & 0.014762 \\
6 & 3.882 & 0.014921 \\
7 & 3.863 & 0.015397 \\
8 & 3.852 & 0.015714 \\
9 & 3.863 & 0.015397 \\
10 & 3.857 & 0.015556 \\
11 & 3.857 & 0.015556 \\
12 & 3.857 & 0.015556 \\
13 & 3.863 & 0.015397 \\
14 & 3.849 & 0.015714 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Temporal evolution of entropy and R\({}_{0}\) values for the generated small world network model. Figure 8: Dynamic entropy (**left**) and R\({}_{0}\) measures (**right**) of the generated small world network. among the considered system constituents. This provided system analysis insights which led to the development of specific metrics for the tailored entropy-based case study. Table 8 illustrates a summarized representation of how information theoretic concepts and their applications were relevant in understanding the case study used. This paper presenting the case study is framed according to the application of information theory concepts with a goal to better understand and assess complex systems. We present the insight drawn from the case study in answering the research question identified i.e., Can information entropy help in quantitatively characterizing a complex system? Because not all complex systems have the same characteristics and behave in a similar fashion, it is indeed not possible to provide a generalized metric to quantitatively characterize a complex system. However, using information theory concepts tailored to the specific system being considered helps to answer and quantify the complexity, based on a set of assumptions. In such a case, a thorough understanding of the considered systems, sub-systems, and their interactions is required. Using the concept of entropy, complex systems can be mapped as a network of interactions, and the characteristics of the complex system can be quantified, thereby setting a foundation for understanding a complex system. The complexity can then be quantified based on a set of assumptions. For example, when a complex system is mapped as a network, information entropy can be used to quantify the network at a given snapshot based on the observed sub-systems' interaction patterns. Considering the network dynamics, at every instant the network emerges with either new nodes introduced into the network or rewiring of the connections among the nodes of the networks. Provided that the data on system interaction patterns at every instance of the system evolution is available, entropy-based measures can detect the precise time instance at which the system is exposed to external stimuli. This is because entropy can be seen as a measure of surprise in which, following sudden external stimuli to the network, a rapid change in the tailored entropy-based measure can be detected when observed over the system dynamics  
The insight drawn is strictly based on the observations from the case study presented in this paper.