##### Compute degree centrality of an undirected graph – Software Engineering

Compute diploma centrality of an undirected graph - Software program Engineering 1. Compute the diploma centrality, betweeness centrality, closeness centrality of nodes within the following graph. 2. A k-regular undirected community is a community by which each vertex has diploma ??. Present that the vector ?? = (1, 1, 1, . . . , 1) is an eigenvector of the adjacency matrix with eigenvalue ??. three. Take into account an undirected tree of n vertices. A specific edge within the tree joins vertices 1 and a couple of and divides the tree into two disjoint areas of n1 and n2 vertices as sketched right here: Present that the closeness centralities ??1 and ??2 of the 2 vertices are associated by four. Calculate the betweenness centrality of the ??^{th}vertex from the top of a "line graph" of n vertices. Right here a line graph on n vertices 1, 2, three,..., n has precisely n - 1 edges that join vertices ?? and ?? + 1, for ?? = 1,..., n - 1. 5. Write a program in your most well-liked programming language to compute diploma centrality of an undirected graph. This system will learn the graph from a file referred to as "graph.txt" and output the diploma centrality of nodes to a file referred to as "diploma.txt". The file "graph.txt" consists of multiples strains by which the primary line accommodates two integers n and m that correspond to the variety of nodes and edges within the graph. Every of the next m strains include two integers u and v, separated by one house, to indicate an edge from u to v. Nodes are numbered from 1 to n. The output file "diploma.txt" accommodates precisely n strains by which the ????h line is the (unnormalized) diploma centrality of node ??. Your submission should embody - The supply file(s) - The pattern enter/output - A README file that describes the compile and operating instruction 6. Write a program in your most well-liked programming language to compute (normalized) closeness centrality of an undirected graph. This system will learn the graph from a file referred to as "graph.txt" and output the diploma centrality of nodes to a file referred to as "closeness.txt". The file "graph.txt" consists of multiples strains by which the primary line accommodates two integers n and m that correspond to the variety of nodes and edges within the graph. Every of the next m strains include two integers u and v, separated by one house, to indicate an edge from u to v. Nodes are numbered from 1 to n. The output file "closeness.txt" accommodates precisely n strains by which the ????h line is the (normalized) closeness centrality of node ??. Your submission should embody - The supply file(s) - The pattern enter/output - A README file that describes the compile and operating instruction