Network Density and Components Analysis

In this exercise, we will delve deeper into the characteristics of social networks by examining the density and components of a network using the Moreno dataset.

Network Density

Network density is a measure that shows the proportion of the observed ties in a network compared to the maximum possible number of ties. It provides an understanding of how interconnected a network is.

In R, we can calculate the density of a network using the gden() function from the network package:

gden(Moreno)

0.08712121

If you’re using the igraph package, you can use the graph.density() or edge_density() functions.

Network Components

A component of a network is a subgroup in which all actors are connected, either directly or indirectly. Identifying components can help us understand the structure and connectivity within the network.

In R, we can find the components of a network using the components() function from the network package:

components(Moreno)

[1] 2

The igraph package also provides a components() function, which gives additional information about each subgroup, including its size and its name.

$membership
 SE  PH  PD  LN  MB  AP  SM  CB TB2 RBW  NW  AL  DB CWB  BS  AC 
  1   1   1   1   1   2   2   3   3   3   3   1   1   1   1   1 
 BW DZM  KW VST  TM  CR AAE HRS LRS  SL  JJ TBC  LE BCL SLL TNB 
  1   1   1   3   3   1   1   1   1   1   4   4   4   1   1   5 
MGE JLG DGT  DK  WT DSW  ME MWB  BD  LL  BB LSM  KM  SP LCP ADE 
  5   5   5   3   3   3   3   1   1   1   1   1   1   6   6   6 
 KH ECS  KT  GB RBH  JU  JZ DSM  BL  CG CSH GGA ADL  DL LBF  GL 
  6   6   6   7   7   7   7   7   1   1   1   1   1   1   1   1 
 CS DSF ALL CW1 DZB  PW ARL  LZ MBM  RW ECW  JK ASS SS1 SMH TB1 
  1   1   1   1   1   1   1   1   1   3   3   3   3   3   3   3 
 DM LBW  MD  TR DSG LRG SS2 JLT LSF TSL LBC LLB  DW 
  3   3   1   5   5   5   3   1   1   1   8   9  10 

$csize
 [1] 47  2 20  3  7  6  5  1  1  1

$no
[1] 10

To access only the number of components, write $no after the components() function.

Exercise

Using the facebook dataset, obtain the density of the igraph object and store this into density. Note that this time the Facebook object is different from the previous exercise.

To download the facebook dataset click: here1

Assume that: