Network Structure

The importance of the networks is being extended to the technological and economic systems, which are becoming in real complex networks. This complexity and the instability of the behaviour of these systems put them in a high risk of turning localized breakdowns that evolve into cascading failures and or financial crisis.
A network analysis of these systems could help us to know what these points of potential breakdown are, and how we can help to solve the conflict. That is why is important to know how the networks looks like, visualizing these systems and making a network analysis of their networks we may found key information that make possible a prediction of the problem, and with time develop solutions that help us to prevent this potential problems.

Most of the measures in networks have their origin in Graph Theory. Graph theory, help us to study the shape of any network (topology of the network) and analyze it mathematically.
Then, there are taken from graph theory different tools to make possible this analysis.

Fig. 1 Weighted and directed Network of the dataset of the characters1 in the novel “Les Miserables” from Victor Hugo.

 

Figure 1, shows the network formed from the relationships that exists among the characters in the novel of Victor Hugo “Les Miserables”. This is the aspect of a network. This network has been made using Gephi, and it will be useful to explain the different elements that constituted a network.
We can find two essential elements in figure 1: nodes and links. Then the figure shows a collection of elements that in this case are the characters of the novel and that are represented by the color circles. The size of the circle represents the importance of this character. Each circle is called “node” in graph theory and network analysis. By other hand, the lines that connect the circles are called the links. The links represents the relationships that exist among two characters. i.e., if there exist a relation among the characters, then one line will be depicted linking them, if not, there not exists this line. The link thickness represents how strong this relation is.

(1) D.E. Knuth, The Standford GraphBase: A platform for combinatorial Computing, Addison-Wesley. Reading, MA (1993).