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# Network Analysis

• July 15, 2023
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Table of Content

A distinct sort of data, known as network data or graph data, necessitates a different kind of analysis.

Key components of a Graph or Network are Vertices /

Adjacency Matrix. is a representation of a network. It should be noted that the adjacency matrix for an undirected graph is symmetric.

There are two types of links or edges between nodes: unidirectional and bidirectional.

##### Node Properties:

Degree Centrality = Number of direct ties with other nodes
In-Degree = Number of Incoming connections
Out-Degree = Number of Outgoing connections

Degree centrality is a local measure and hence we should look at other measures.

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##### Closeness Centrality is how close the node is to other nodes in the network

Closeness Centrality = 1/(sum of distances to all other nodes)

When a comparison of two networks arise then normalized closeness should be considered

Normalized Closeness = (Total number of nodes - 1) * Closeness

A node's or an edge's betweenness centrality can be determined.

How frequently a node or edge is on the shortest path between pairs is known as betweenness centrality.

We utilise normalised Betweenness to compare two networks.

Instead than merely counting the number of connections you have, eigenvector centrality counts the quality of your connections.

• Nodes which are connected to high scoring nodes contribute more to the score of that nodes which are connected to low scoring nodes.
• Eigenvector is calculated from eigenvectors of adjacency matrix.

• X corresponding to the highest Eigenvalue is the vector that consists of the Eigenvector centralities of the nodes.
• Diffusion Centrality is a measure on how likely is a person, who receives the information, going to diffuse the information further.