Network analysis using Big Study data

Data preparation

Read interpersonal network data

Each person interviewed has two csv files, one has the name FirstnameLastname.csv, the other the name FirstnameLastnameOrgs.csv. The first has data on relationships with other invividuals, the second relationships with other organizations.
DO NOT PUT OTHER csv FILES IN THE DIRECTORY

Data is taken from each component of the list and combined.

Add attribute data

## [1] "Name"             "OrganizationName" "Interviewed"     
## [4] "OrganizationID"   "Profession"

Create igraph objects

## IGRAPH DN-- 78 1694 -- 
## attr: name (v/c), Knows (e/n), Strength (e/n), advice (e/n),
##   leadership (e/n), influence (e/n)

Initial analysis of 'Known' network

Advice network

## IGRAPH DN-- 78 504 -- 
## attr: name (v/c), Name (v/c), OrganizationName (v/c), Interviewed
##   (v/c), OrganizationID (v/n), Profession (v/n), Knows (e/n),
##   Strength (e/n), advice (e/n), leadership (e/n), influence (e/n)

Leadership network

How hierarchical are the networks?

Use a measure called the global reach centralisation. Based on out-ties, this is likely to be high for the full networks, as out-ties are restricted to the people interviewed (22 out of 78).

GRC for Knows: 0.7178

GRC for Advice: 0.6612

GRC for Leadership: 0.6895

Same again, but without isolates

These figures suggest a high degree of hierarchy, but this is almost certainly because only 22 of the 78 network members were interviewed, so they are the only ones with out-degrees.

GRC for Knows: 0.7237

GRC for Advice: 0.7

GRC for Leadership: 0.7123

Use only subnetworks of people who were interviewed

First, need to generate the subnets, then plot them.

GRC for Knows: 0

GRC for Advice: 0

GRC for Leadership: 0

All of these networks have no hierarchy according to the global reach centrality measure. This should be confirmed by a dyad census, which should show many mutual ties. In each network there are 22 people, so (22² - 22)/2 = 231 pairs. This is used to express numbers of types of dyad as a proportion.

As we would expect, much less reciprocity in advice than knows and less still in leadership. There is some evidene of status hiearchy in this, so think about other ways of investigating this.

Do people who give advice ask for advice from the people to whom they have given it?

Correlation between in-degree and out-degree shows if people who ask lots of others for advice don't get asked for advice by a lot of people, and vice versa.

Reciprocity depends on working out the expected number of mutual ties given the total number of ties in the network. So, this is conditioning on the number of ties (an alterative to proportion of reciprocal ties is to total possible ties shown above).

Finally, can look at cyclicality, number of cycles as proportion of triads with at least 2 parts of the cycle.

These measures are all quite high, and suggest that there is a high degree of mutual support in the network. This is particularly evident in the advice network, although even people who are identified as leaders often reciprocate the identification.

Structural equivance in advice network

Another approach to investigating networks is to look for evidence of equivalent groups. These would be groups of respondents who have similar patterns of ties to other respondents.

Looking just at in ties (get approached for advice)

##   DianeHobday     KathJones LouiseLeather    PankajShah 
##             1             5             3             2

##     AmandaDunne    DotGillespie RachaelWilliams 
##               7               9               8

##       AnnSmallman     CarolynBishop      ClaireThomas     DuncanRandall 
##                13                15                17                14 
##      EmmaAspinall     FionaReynolds          JaneCoad      JaneHoughton 
##                16                11                16                 9 
##        JimTindall NicolaFitzmaurice     RachelBloomer         SarahKirk 
##                15                18                 9                12 
##   StephanieCourts         SueDavies        SueEdwards 
##                13                11                11

This seems to show three structurally equivalent groups, the first two of which are less approached for advice than the others. (Jane Houghton and Rachel Bloomer are exceptions as they have only 9 nominations, but are in third cluster.)

Looking just at out ties (approach others for advice)

##   DianeHobday     KathJones LouiseLeather    PankajShah 
##             5             6             4             1

##       AmandaDunne       AnnSmallman     CarolynBishop      ClaireThomas 
##                14                16                17                16 
##      DotGillespie     DuncanRandall      EmmaAspinall     FionaReynolds 
##                 5                15                13                11 
##          JaneCoad      JaneHoughton        JimTindall NicolaFitzmaurice 
##                11                 6                11                17 
##   RachaelWilliams     RachelBloomer         SarahKirk   StephanieCourts 
##                10                11                10                12 
##         SueDavies        SueEdwards 
##                14                10

People who get asked for advice least also ask for advice least.

Looking both type of ties together

##   DianeHobday     KathJones LouiseLeather    PankajShah 
##             6            11             7             3

## DotGillespie JaneHoughton 
##           14           15

##       AmandaDunne       AnnSmallman     CarolynBishop      ClaireThomas 
##                21                29                32                33 
##     DuncanRandall      EmmaAspinall     FionaReynolds          JaneCoad 
##                29                29                22                27 
##        JimTindall NicolaFitzmaurice   RachaelWilliams     RachelBloomer 
##                26                35                18                20 
##         SarahKirk   StephanieCourts         SueDavies        SueEdwards 
##                22                25                25                21

ergm advice

Structural equivance in leader network

Looking just at in ties (nominated as leaders)

##     AmandaDunne RachaelWilliams       SarahKirk StephanieCourts 
##               7               7              11              11

## DianeHobday   KathJones 
##           1           5

## LouiseLeather    PankajShah RachelBloomer    SueEdwards 
##             3             4             5             8

##       AnnSmallman     CarolynBishop      ClaireThomas      DotGillespie 
##                14                15                16                10 
##     DuncanRandall      EmmaAspinall     FionaReynolds          JaneCoad 
##                10                17                15                15 
##      JaneHoughton        JimTindall NicolaFitzmaurice         SueDavies 
##                10                11                19                10

Regular equivalence

## Vertex sequence:
## [1] "AmandaDunne"   "AnnSmallman"   "DotGillespie"  "EmmaAspinall" 
## [5] "LouiseLeather" "SueEdwards"

## Vertex sequence:
## [1] "CarolynBishop"     "ClaireThomas"      "NicolaFitzmaurice"
## [4] "SarahKirk"         "StephanieCourts"   "SueDavies"

## Vertex sequence:
## [1] "DianeHobday" "KathJones"

## Vertex sequence:
## [1] "DuncanRandall"   "JaneCoad"        "JaneHoughton"    "JimTindall"     
## [5] "PankajShah"      "RachaelWilliams"

## Vertex sequence:
## [1] "FionaReynolds"

## Vertex sequence:
## [1] "RachelBloomer"

## Error: invalid 'name' argument

Plot blockmodel

Read organization network data