# Network Analysis

If I call the name of this page particularly, it is "Analysis of the **structure** of the network."

The structure is the important point to use network.

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Simple Model of Network

The set of node and edge is the simple model of the network.

It is very simple, but the famous peculiarity of the network ("Small world" and "Scale free") is the phenomena of this model.

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Density

If there are many edges but not many nodes, it means that density is high.

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Distance

The model uses "1" and "0".
The length of the edge does not have meaning.

In this model, the distance between A and B is 1.
B and C is 1.
A and C is 2 (= 1 + 1).

In this model ditance and the number of steps are same.

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Degree

The number of edges from the node is "degree".

The degrees of A and C are 1. B is 2.

In the real network, there are many number of degress.
The node with large degree is called "hub".

Power law of degrees is found in many type of networks.
It is called "**scale free**".

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Small World

Small world is known that average of distance to the unknown people is not so long.

Real network is the network of clsuter (dense and small network).
If there are short cuts, the average of distance is short.
This law was found as the cause of the small world.

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More Information to the Model

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Range of Relationship

The simple model uses only 1 and 0.
If we use the range of this index, we can use more complex model.

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Weak Ties

"Tie" is the name of edge in the field of society analsys.

Cluster is also the network of strong ties.

In the network science many people study the power of weak ties.

Weak ties are not so important in the daily life.
But it is important to get precious information.

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Size of Nodes

The size of nodes are used.
For example, in
Text Mining

NEXT Eigenvalue Analysis