Network Study

Basic network properties based on the first ten respondents (shown as the first ten in the tables, identified in red on the plots).

Ideas for analysis

• looking for sub-groups
• looking for gaps
• looking for stars and isolates
• looking at strength of ties, how does that compare
• looking at pattern of advice; can we identify knowledge brokers?
• what's the leadership structure?
• influential outside network? Different from leaders?
• are there bottlenecks?
• bridges or brokers? what and who?
• density? centrality?
• two-mode network?

Summary of the complete network

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

Problems with data.

1. In some data sheets Rachael Williams spelt Rachael Wiliams (only one l)
2. Sue Edwards sometimes spelt Su Edwards

“Is this person known to you?”

Summary of the network

IGRAPH DN-- 78 824 -- 
attr: name (v/c), Name (v/c), Interviewed (v/c), colour (v/c),
  Knows (e/n), Strength (e/n), advice (e/n), leadership (e/n),
  influence (e/n)

Graph of the network

In-degrees

deg.know Freq
1 0 1
2 1 2
3 2 3
4 3 5
5 4 6
6 5 4
7 6 6
8 7 3
9 8 4
10 9 3
11 10 4
12 11 4
13 12 4
14 13 4
15 14 2
16 15 4
17 16 3
18 17 2
19 18 1
20 19 2
21 20 3
22 21 5
23 22 3

“Would you go to this person for advice?”

Summary of the network

IGRAPH DN-- 78 507 -- 
attr: name (v/c), Name (v/c), Interviewed (v/c), colour (v/c),
  Knows (e/n), Strength (e/n), advice (e/n), leadership (e/n),
  influence (e/n)

In-degrees

% latex table generated in R 2.15.1 by xtable 1.7-0 package
% Sun Jul 01 17:05:08 2012
\begin{table}[ht]
\begin{center}
\begin{tabular}{rlr}
\hline
& Degree.deg.adv & Degree.Freq \
\hline
1 & 0 & 4 \
2 & 1 & 11 \
3 & 2 & 5 \
4 & 3 & 6 \
5 & 4 & 10 \
6 & 5 & 7 \
7 & 6 & 4 \
8 & 7 & 5 \
9 & 8 & 4 \
10 & 9 & 2 \
11 & 10 & 4 \
12 & 11 & 5 \
13 & 14 & 1 \
14 & 15 & 3 \
15 & 16 & 1 \
16 & 17 & 2 \
17 & 19 & 1 \
18 & 20 & 2 \
19 & 21 & 1 \
\hline
\end{tabular}
\end{center}
\end{table}

“Does person occupy leadership role?”

Summary of the network

IGRAPH DN-- 78 443 -- 
attr: name (v/c), Name (v/c), Interviewed (v/c), colour (v/c),
  Knows (e/n), Strength (e/n), advice (e/n), leadership (e/n),
  influence (e/n)

Graph of the network

In-degrees

“Do you see the person as influential outside network?”

Summary

IGRAPH DN-- 78 378 -- 
attr: name (v/c), Name (v/c), Interviewed (v/c), colour (v/c),
  Knows (e/n), Strength (e/n), advice (e/n), leadership (e/n),
  influence (e/n)

Graph of the network (isolates removed)

In-degree

Summary of all in-degrees

Community structure.

Communities are highly connected between them but with few links to other vertices. Calculate walktrap community using the advice nextwork, with isolates removed. This uses a random walk algorithm to identify communities. Pascal Pons, Matthieu Latapy: Computing communities in large networks using random walks, http://arxiv.org/abs/physics/0512106.

Edge betweenness centrality

Network characteristics

Have to restrict to ties between respondents only.

dens <- function(g) {
    n.edge <- ecount(g)
    n.vert <- vcount(g)
    e.max <- n.vert^2 - n.vert
    if (is.directed(g)) {
        n.edge/e.max
    } else {
        n.edge/(e.max/2)
    }
}

Density of knows network: 0.7165
Density of advice network: 0.4848
Density of leadership network: 0.4805
Density of influence network: 0.3939

Leader network, interviewed people only

Dyad censuses

          Mutual Asymmetric Null Total Density
Knows        144         43   44   331  0.7165
Advice        78         68   85   224  0.4848
Leader        65         92   74   222  0.4805
Influence     49         84   98   182  0.3939

In-degree

      AmandaDunne       AnnSmallman     CarolynBishop      ClaireThomas 
                6                13                14                21 
      DianeHobday      DotGillespie     DuncanRandall      EmmaAspinall 
                0                11                10                18 
    FionaReynolds          JaneCoad      JaneHoughton        JimTindall 
               14                21                11                19 
        KathJones     LouiseLeather NicolaFitzmaurice        PankajShah 
                4                 3                19                 1 
  RachaelWilliams     RachelBloomer         SarahKirk   StephanieCourts 
                4                 2                 7                10 
        SueDavies        SueEdwards 
                6                 8 

In the leadership network, there is a group of five people who seem to be most prominent. This network is quite centralized, suggesting a form of hierarchical structure.

Centralization scores, in-degree

     Know    Advice    Leader Influence 
   0.2835    0.4199    0.5195    0.5584 

Centralization scores, betweenness

     Know    Advice    Leader Influence 
  0.03828   0.08451   0.07461   0.26069