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  • Network theory is a way of describing the world in terms of a model called a network

  • that allows us to capture the information about the relationship between things. But

  • lets first think about why we might be interested in this at all.

  • We often describe the world in terms of objects or things and their properties, we talk about

  • countries and their GDP, people and their age or the color of a car, this type of component

  • based analysis works well when the system we are interested in is relatively isolated.

  • But when we turn up the interactions and connectivity between elements within a system it is increasingly

  • the connections that come to shape the elements and define the system as a whole and thus

  • we need a model that captures this information about the relationships and allows us to reason

  • about it, this is where network theory comes in.

  • Network theory starts with a very simple view of the world as made up of nodes which are

  • things or objects, like people, cities, computers etc. and the relationships between these things,

  • called edges, such as friendships, trading partners, cables and so on.

  • This abstract representation of the world, can be used to model a wide variety of things,

  • thus we can have social networks, biological networks consisting of interacting creatures

  • within an ecosystem or logistic networks composed of interacting suppliers and consumers.

  • Network theory gives us a set of tools for analyzing the individual elements and relations

  • within these networks, the structure of the network and the properties that these different

  • networks structures give rise to.

  • The first set of question we might like to ask about a particular network relate to its

  • degree of connectivity, that is how connected an individual element or the wholes network

  • is, this will tell us many things about it such as how quickly a new event could spread

  • or propagate through the system.

  • The average degree of connectivity will give us a quick answer to this; this is calculated

  • by taking the total number of edges and dividing it by the total number of nodes within the

  • network

  • We also need to take into account how large the network is, that is to say how far is

  • it on average from one point to another. This is called the average path length and we can

  • calculate it by taking the average of all the path length between all the nodes.

  • Because networks are all about connectivity we often ascribe value to individual nodes

  • based upon their degree of connectivity, there are various methods for calculating this but

  • a popular one called Eigenvector centrality, which measures both how many edges a node

  • has and how connected the nodes it joined to are also.

  • Popular web search engines use variants of this Eigenvector centrality measure to rank

  • webpages by calculating both the number of links into a webpage and the degree of connectivity

  • of the pages that link into them thus gaining an idea of the relative importance of the

  • website

  • Next we are interested in talking about the overall structure to the network this will

  • be largely determined by how the relationship between the nodes was formed.

  • If the relations between elements was generated randomly we would expect a relatively even

  • distribution of edges across the network, this type of structure or topology is called

  • a distributed network as the relative importance of any node is distributed across the entire

  • network.

  • A second type of network structure we can get is called decentralized or small world,

  • this is generated by having local clusters of connections, but also having some random

  • distant connections.

  • an example of this might be a group of friends, with some of the friends having distant relatives

  • in other parts of the world. By using these local connection within the group and distant

  • connections research has shown that it is possible to connect two random people within

  • a average of just six steps and thus it is termed small world.

  • Lastly we have more centralized networks called scale free networks, this is where may nodes

  • have chosen to connect to the same node giving it a degree of connectivity that greatly exceeds

  • the average whilst leaving may with a very low level of connectivity.

  • Many real networks are through to be scale-free, including social, biological and technological

  • systems such as world-wide web, where very few sites like Wikipedia have a very large

  • amount of links into them, whilst the vast majority of websites have very few.

  • These various types of network structures give rise to different properties, a key question

  • we are interest in asking here is how robust or fragile is a particular type of network

  • as this will not only help us understand networks better, but will also be of great significance

  • in how we design and manage them.

  • For example, think about a country with many small to medium size cities supplying the

  • population with various public services, if we were to remove one of the cities it would

  • have a limited effect on the overall system, because the networks has a distributed structure

  • making it robust to fail of this kind.

  • In contrary if we take a county with one dominant capital city with the rest of the urban network

  • dependent upon it for core services, this centralized network may be more efficient

  • but it is also in what is called a more critical state as effecting this single primary node

  • would have a large systemic effect.

  • As we transit from an industrial to information societies, networks are emerging as a new

  • paradigm in how we structure our systems of organization both social and technological.

  • Network theory is a young and rapidly growing area that provide us with a set of tools for

  • designing and managing these new types of organization and more generally understanding

  • the world around us from a different perspective.

Network theory is a way of describing the world in terms of a model called a network

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網絡理論概述 (Network Theory Overview)

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    Josh 發佈於 2021 年 01 月 14 日
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