Network theory is an area of computer science and network science and part of graph theory. It has applications in many disciplines, including statistical physics, particle physics, computer science, biology, economics, operations research, and sociology. Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more generally, asymmetric relations between discrete objects.
Applications of network theory include logistical networks, World Wide Figure 3.14 Line of sight inter-visibility
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Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, and so on.
Network Analysis
Geospatial data are interrelated. In nature itself, the different geological structures are related to each other in some pattern. GIS systems use a layered approach of data storage and representation to exhibit these interrelations and patterns. They deal with the interrelated nature of geographic data; some data have specialized rules and parameters, and restrictions on interaction and analysis must occur within this framework. There is a requirement of a data model that can represent relationships and the interconnectivity of spatial data. Graph theory is a field of discrete mathematics that can represent this interconnectivity.
Graph is a collection of edges and nodes that represent interconnected objects. Graph theory studies all types of networks. The associated numbers represent characteristics of connectivity.
Network analysis focuses on edge–node topology to represent real-life networks of information, which include driving directions, multimodal routing, information networks, electricity, water, sewer, and natural gas lines (Figure 3.15).
Edges and nodes
Edges connect a series of nodes. A node may be a start or end point for an edge. Each node touches at least one edge. Nodes have one or more edges connecting them. GIS needs to know what data are parts of the network and what are not. OpenStreetMap is a free world map whose routing software follows the same rules as that of the edge–node network. The GDB stores additional information about the network and its parts, which includes information about the types of network edges, connectivity rules, and impedance.
In the case of ArcGIS (mapping and analysis tool of the ESRI), the edge–node topology is enforced by the base network. The base network within ArcGIS is the geometric network that follows the edge–node topology. Once the network is complete, one can perform analysis on it. For example, one can check the shortest cost path for networked flow, service areas routing connectivity analysis, and the health of the network.
A network is a set of interconnected linear features that form a pattern or framework. It is commonly used for moving resources from one location to another. City streets, power transmission lines, and
airline service routes are examples of networks. Network analysis is a GIS analysis technique characterized by the use of feature networks.
Feature networks are almost entirely composed of linear features.
Transportation networks and watershed networks are prime examples.
Two examples of network analysis techniques are as follows: allocation of values to selected features within the network to determine capacity zones and determination of the shortest path between connected points or nodes within the network based on attribute values. This is often referred to as route optimization. Attribute values may be as simple as minimal distance or more complex involving a model using several attributes to define rate of flow, impedance, and cost. Network analysis provides techniques to determine optimum path in a network using certain decision rules.
The limitations on the ability to perform network analysis in early GIS data structures have necessitated the development of pure network data models. These include non-planar data structures that relax planarity requirements to model real-world networks in a more realistic way.
There are several advancements in network GIS that could improve the ability to research network-based problems in the near future. The network is a compelling research paradigm because its form can so intuitively represent complex systems.
Figure 3.15 Network analysis
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EXERCISES Short Answer Questions
1. What is attribute data? Define different methods to store attribute data.
2. What is relation in RDBMS?
3. What is data overlay?
4. What is classification?
5. Explain buffer.
6. How is GIS different from other computer-based information systems?
7. How do we capture data for GIS? What is the difference between primary and secondary data acquisition methods?
8. What do union, intersection, and identity mean?
9. Explain the importance of network analysis in GIS.
10. What is aggregation function in GIS?
Descriptive Questions
1. Explain RDBMS. How does GIS support relational database structure?
2. Define GIS functionality. Explain the different steps in GIS functionality.
3. Explain generalization and different generalization operations in GIS.
4. Spatial analysis function is the core of GIS. Explain.
5. Explain different types of vector- and raster-based overlay techniques.
REFERENCES
Croswell, P. 1991. Obstacles to GIS implementation and guidelines to increase the opportunities for success. Journal of the Urban and Regional Information Systems Association 3(1): 43–57
Foote, K. E. and D. J. Huebner. 1996. Managing error. Details available at
<www.colorado.edu/geography/gcraft/notes/manerror/manerror_f.
html>
Hägerstrand, T. 1973. The domain of human geography. In Directions in Geography, edited by R. J. Chorley, pp. 67–87. London: Methuen Wilson, A. G. and R. J. Bennett. 1985. Mathematical Methods in Human
Geography and Planning. London: Wiley