关于数据挖掘:R语言代做编程辅导ASSIGNMENT-FOUR-RANDOM-GRAPHS附答案

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PROBLEM 1) Creating Random Adjacency Matrices

Script Name: adjMatrix
Input:

    n... The number of vertices in the graph
    p... Probablity two vertices are connected
    plot... whether or not the matrix should be plotted as a graph

Output: The nxn matrix of zero and ones
Error Checking: The dimension is postive (else return NULL)

Description: The matrix is related to a simple, undirected graph of n vertices.
In the graph is Vertex i and Vectex j are joined by an edge, then in the matrix
A[i,j] = 1, if no edge exists then A[i,j]=0. There are differenct ways of handling
the diagonal. We will require the diagonal elements to be NA.

The matrix must be symmetric. That is A[i,j]=A[j,1]

Whether or not an entry in the matrix is 0 or 1, is determined by drawing numbers
from the binomial distribution. This distribution will yield a 1 with probability p and a
o with probability (1-p). In R it will work like this, in the ith column (vertex i)
, we require A[i,i] to be NA. This leaves n-1 entries to be determined. We
use the command rbinom(n-1,1,p) to general these entries all at once, or
rbinom(1,1,p) to generate them one at a time.

Plot: Using igraph create a simple plot. Use a color easy on the eyes such
as something found in the Brewer color palette (discussed in class)

requires(igraph)

adjMatrix<-function(n,p,plot=FALSE)
{m=matrix(1,n,n)
  for(i in 1:n){for(j in 1:n){if(i<j){m[i,j]=ifelse(i==j,NA,rbinom(1,1,p) )
        m[j,i]=m[i,j]
      }
    }
  }
  colpal<-brewer.pal(8,"Dark2")  
  
  gA <- graph.adjacency(m, mode="undirected",diag=FALSE)
  V(gA)$color<-colpal[1]   You choose 1 to 8... try some others
  plot(gA, layout=layout.auto,main="Random Graph using Brewer Color Palette")
  s
}

PROBLEM 2) Person with the most friends in the network

Script Name: vowelMax
Input:

    A... An adjacency matrix
    plot... Plot the graph with the "friends" network highlighted

Output: The number of the vertex with the most edge connections
Error Checking: None

Description: The number of “friends” a person has in a network is the
number of edges connected to that vertex. The ith person
in the network, will be connected to the jth person if A[i,j]=1. So the
number of 1’s in the ith column reports how many edges connect person i to others
In mathematical terms, this is called the “degree” of vertex i.

So you must determine the number of ones in each column and then find
which column has the most ones.

Hint: There is a quick trick to use here. Since a column has only
0 or 1 in it, the sum of all of the numbers in the column is the same
as the number of 1’s in the column. Prove that to yourself.

Plot: Use igraph to plot the graph. Use three colors for the vertices: one
for the most friendly person, another for his/her immediate friends, and another
for the remaining vertices. Color red the edges from the most friendly person to
his/her friends. All remaining edges are black.

mostFriends<-function(A,plot=FALSE)
{A[is.na(A)]=0
  s=which(apply(A,2,sum)==max(apply(A,2,sum)))
  n=which(A[,s]==1)
  pastel<-brewer.pal(8,"Pastel2")   Try a different palette      
  gA <- graph.adjacency(A, mode="undirected",diag=FALSE)
  V(gA)[n]$color<-pastel[1]
  V(gA)[s]$color<-pastel[2]   changes the 5 vertex to the 4th color of the palette
  V(gA)[n]$color<-pastel[3]
  E(gA)[s%--%n]$color<-"red"
  plot(gA, layout=layout.auto,main="Random Graph With A Range of Vertices Colored")
  s
}

PROBLEM 3) Find a lonely person

Script Name: noFriends
Input:

    A... An adjacency matrix

Output: The number of the vertex with the no edge connections
Error Checking: None

Description: The number of “friends” a person has in a network is the
number of edges connected to that vertex. The ith person
in the network, will be connected to the jth person if A[i,j]=1. So the
number of 1’s in the ith column reports how many edges connect person i to others
In mathematical terms, this is called the “degree” of vertex i.

So you must determine the number of ones in each column and then find
which column has the most ones.

Hint: There is a quick trick to use here. Since a column has only
0 or 1 in it, the sum of all of the numbers in the column is the same
as the number of 1’s in the column. Prove that to yourself.

Plot: Create a plot of the graph using igraph. Make the “lonely” person/people a
different color

noFriends<-function(A,plot=FALSE)
{s=which(apply(A,2,sum)==0))

PROBLEM 4) Number of friendship relationships in the network

Script Name: numFriendships
Input:

    A... An adjacency matrix

Output: The number of uniqe edges in the graph

Description: The number of friendships in the network is the number of edges

in the graph.  Basically, count the ones in the adjacency matrix, but be
careful.  (Remember, an edge from i to j is the same as an edge from j to i)

numFriendships<-function(A)
{num}

PROBLEM 5) Add a person to the friendship network

Script Name: addPerson
Input:

    A... An adjacency matrix
     p... Probability a relationship forms
     plot... Show the new person and relationships

Output: New adjacency matrix

Description: As in creating an adjacency matrix, a new column is added
and the binomail distribution is used to determine the 1 entries.

Plot: Plot the graph using igraph. Use three colors for the vertices: one
for the newly added person, another for his/her immediate friends, and another
for the remaining vertices. Color red the edges from the new person to
his/her friends. All remaining edges are black.

addPerson<-function(A,p,plot)
{n=nrow(A)
  new=rep(1,n)
  for(i in 1:n){new[i]=rbinom(1,1,p)
  }
  A=cbind(A,new)

PROBLEM 6) Add several people to the friendship network

Script Name: growNetwork
Input:

    A... An adjacency matrix
     p... Probability a relationship forms
     n... the number of people to add
     plot... Show the new person and relationships

Output: New adjacency matrix

Plot: Plot the graph using igraph. Use three colors for the vertices: one
for the newly added person, another for his/her immediate friends, and another
for the remaining vertices. Color red the edges from the new person to
his/her friends. All remaining edges are black.

growNetwork<-function(A,n,p,plot=FALSE)
{row=nrow(A)
  for(ii in 1:n){nn=nrow(A)
    new=rep(1,nn)
  for(i in 1:nn){new[i]=rbinom(1,1,p)
  }