# Quantitative Characterization of Complex Systems--An Information Theoretic Approach
## 4 Complex Networks--An Overview and Definition  
A network, as derived from graph theory, is a simplest form representing a collection of points that are joined together in pairs by lines. In every such representation, the set of points are referred to as nodes or vertices, and the lines used to connect the points together are referred as edges. Networks can be mapped from contexts across several domains, such as physical sciences, biological sciences, and social sciences, that consist of several components linked together. It is observed in the literature that physical, biological, and social systems, when mapped as networks, often provide new insights into the behavior and structure of the system in question [21]. The question of when a considered network is said to be complex can be addressed using the principles of complexity science. Several contrasting views [22; 23; 24; 25; 26] on complex and complicated systems have been defined throughout the literature from the lens of complexity science. Drawing upon the views of various researchers on characteristics of complicated and complex systems and, looking back into networks topologies and their characteristics [21], in this study a complex network is defined as a network mapped from a system that primarily constitutes interactions observed among systems components, interactions of human actors in the system, and the influence of human interaction on system components. Continual human interactions in such networks play a primary role in influencing the network structure and its evolution. The inherent ambiguity of human interactions and their individual perceptions introduce non-linear behavior, emergence, and self-organization in networks, thereby introducing complexity. Table 1 illustrates the distinguishing characteristics of complicated and complex networks.  
Figure 2 summarizes an abstract fundamental representation of how we define a complex network. Complexity in a network is illustrated as result of the continual relationship between an actor (human) and the components (sub-systems) of a system; that is, complexity in a network depends upon the extent of interactions a human actor has in a system and the cascading influence human interactions initiate throughout that lead to network emergence.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Complicated Networks** & **Complex Networks** \\ \hline Nodes & Structured and predefined set of connections & Entity of random node connections \\ Characteristic & Highly tuned & Minimally tuned \\ Topology & Highly organized structure & Continually emergent structure based on dynamics of interactions \\ Robustness & Robust to targeted perturbations & Robust to random perturbations \\ Relationships & Easier to understand network & Difficult to understand network \\  & relationships & relationships \\ Human influence & Human interactions based on a predefined set of rules & Random human interactions \\  & Software system, automotive system, electronic circuit networks & Transportation, social, communication \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristics of complicated and complex networks.  
To some extent, complex networks can be characterized by the interactions among its constituent nodes. These interactions evolving together result in the dynamic nature of the network. Many complex networks have a number of properties that are common in nature, leaving aside their domain specific characteristics. Displaying small world phenomena is one such characteristic, and the other is the highly heterogeneous nature of interaction patterns in many cases [27]. Heterogeneity in complex networks can be characterized by observing the degree distribution based on the node interaction dynamics. Many observed networks are reported to be scale-free networks, in which the degree distributions are observed to follow a power law. Examples of such networks are electronic circuits, cellular metabolism networks, research collaboration networks, and connectivity in the World Wide Web [28].