30 - Compute the Detour Index and the measure of network density for a given network

Compute the Detour Index and the measure of network density for a given network

Concepts

  • [AM11-2] Graph theoretic descriptive measures of networks
    Identifying and listing all elements does not describe a system in full. There may be many different ways in which elements may be connected or related to each other. The interactions, relationships between elements are essential to describe a system. Relationships between elements can be described by two types of flows: flows of material, and flows of information. Material flows connect elements between which there is an exchange of some substance. This can be some kind of material (water, food, cement, biomass, etc.), energy (light, heat, electricity, etc.), money, etc. It is something that can be measured and tracked. Also if an element is a donor of this substance the amount of substance in this element will decrease as a result of the exchange, while at the same time the amount of this substance will increase in the receptor element. There is always a mass, or energy conservation law in place. Nothing appears from nothing, and nothing can disappear to nowhere. The second type of exchange is with an information flow. In this case element A gets information from element B. Element B at the same time may have no information about element A. Even when element A gets information about B, B does not lose anything. Information can be about the state of an element, about the quantity that it contains, about its presence or absence, etc. Information flows can be used to describe rules and policies. Information flows can modify the rates of flow between elements, they can switch certain processes and interactions on and off. But the process through which policies, interventions and norms for action are established, and could for example define the values of such information flows, are themselves the result of social interaction between relevant stakeholders from public, private or civil society. The simplest is to acknowledge the existence of a relationship between certain elements, like this is done in a graph. In a graph a node presents an element and a link between any two nodes shows that these two elements are related. However there is no evidence of the direction of the relationship: we do not distinguish between the element x influencing element y or vice versa. This relationship can be further specified by an oriented graph that shows the direction of the relationship between elements. An element can be also connected to itself, to show that its behaviour depends on its state. We can further detail the description by identifying whether element x has a positive or negative effect on element y. With networks, interesting questions arise that have to do with connectivity and network capacity. These relate to applications such as traffic monitoring and watershed management. With network elements—i.e. the lines that make up the network—extra values are commonly associated, such as distance, quality of the link or the carrying capacity.