# R社会网络分析教程四

> # LAB 4: Centrality #
> # NOTE: if you have trouble because some packages are not installed,
> # see lab 1 for instructions on how to install all necessary packages.
> #############################################################
> # Lab 4
> # The purpose of this lab is to acquire centrality measures,
> # to determine how they are interrelated, and to discern
> # what they mean.
> ##############################################################
> ###
> # 1. SETUP
> ###
> library(igraph)
> ###
> # 2. LOAD DATA
> ###
> # This lab uses SSL.dat (social interaction) and TSL.dat (task
> # interaction) from the S641 Semester 1 class in student_nets.
> # The class is a biology 2 class at a public high school.
>
> # load data:
> data(studentnets.S641, package = "NetData")
>
> # Reduce to non-zero edges and build a graph object
> s641_full_nonzero_edges <- subset(s641_full_data_frame, (social_tie > 0 | task_tie > 0))
ego alter social_tie task_tie
5    1     5      5.625     0.00
6    1     6      1.500     0.00
22   1    22      1.875    11.25
44   2    22      0.375     2.25
74   4     8      1.875     0.75
89   5     1      5.250     0.00
>
> s641_full <- graph.data.frame(s641_full_nonzero_edges)
> summary(s641_full)
Vertices: 21
Edges: 79
Directed: TRUE
No graph attributes.
Vertex attributes: name.
Edge attributes: social_tie, task_tie.
>
> # Create sub-graphs based on edge attributes and remove isolates
> s641_social <- delete.edges(s641_full, E(s641_full)[get.edge.attribute(s641_full,name = "social_tie")==0])
> s641_social <- delete.vertices(s641_social, V(s641_social)[degree(s641_social)==0])
> summary(s641_social)
Vertices: 19
Edges: 57
Directed: TRUE
No graph attributes.
Vertex attributes: name.
Edge attributes: social_tie, task_tie.
>
> s641_task <- delete.edges(s641_full, E(s641_full)[get.edge.attribute(s641_full,name = "task_tie")==0])
Vertices: 20
Edges: 48
Directed: TRUE
No graph attributes.
Vertex attributes: name.
Edge attributes: social_tie, task_tie.
>
> # Look at the plots for each sub-graph
> social_layout <- layout.fruchterman.reingold(s641_social)
> plot(s641_social, layout=social_layout, edge.arrow.size=.5)
>
> # Note: click on the graph and then use the drop down menu to
> # save any plot you like -- it will save as a pdf.
>
>
> # Question #1 - what can you say about network centralization from these graphs?
>
> ###
> # 3. CALCULATE CENTRALITY MEASURES FOR SOCIAL
> ###
>
> # Indegree centrality measures how many people direct social
> # talk to the individual.
> indegree_social <- degree(s641_social, mode=’in’)
> indegree_social
[1] 3 1 1 3 3 1 1 1 2 2 3 1 5 4 7 5 3 5 6
>
> # Outdegree centrality measures how many people the actor directs
> # social talk to.
> outdegree_social <- degree(s641_social, mode=’out’)
> outdegree_social
[1] 3 1 1 3 3 1 1 1 2 1 3 1 5 4 6 6 3 4 8
>
> # Closeness is the mean geodesic distance between a given node and
> # all other nodes with paths from the given node to the other
> # node. This is close to being the mean shortest path, but
> # geodesic distances give higher values for more central nodes.
> #
> # In a directed network, we can think of in-closeness centrality
> # as the average number of steps one would have to go through to
> # get TO a given node FROM all other reachable nodes in the
> # network. Out-closeness centrality, not surprisingly, measures
> # the same thing with the directionality reversed.
>
> # In-closeness centrality
> incloseness_social <- closeness(s641_social, mode=’in’)
> incloseness_social
[1] 0.16363636 0.15652174 0.05555556 0.16363636 0.15000000 0.13533835
[7] 0.05555556 0.13533835 0.15000000 0.22500000 0.16513761 0.18947368
[13] 0.17475728 0.16216216 0.17821782 0.17142857 0.16071429 0.17142857
[19] 0.17647059
>
> # Out-closeness
> outcloseness_social <- closeness(s641_social, mode=’out’)
> outcloseness_social
[1] 0.23684211 0.22222222 0.05555556 0.23684211 0.20454545 0.16981132
[7] 0.05555556 0.17475728 0.19780220 0.05555556 0.23076923 0.05555556
[13] 0.25714286 0.22500000 0.23684211 0.25352113 0.22222222 0.24657534
[19] 0.27272727
>
> # Betweenness centrality measures the number of shortest paths
> # going through a specific vertex; it is returned by the
> # betweenness() function. (Recall that in the previous lab we used
> # a related measure called edge betweenness, which is returned by
> # the edge.betweenness() function.)
> betweenness_social <- betweenness(s641_social)
> betweenness_social
[1]  24.0000000   0.0000000   0.0000000  24.0000000  28.0000000   0.0000000
[7]   0.0000000   0.0000000  28.0000000  15.0000000  52.0000000   0.0000000
[13]  45.8333333   0.8333333  33.0000000  14.7500000   0.2500000  13.5000000
[19] 126.8333333
>
> # Eigenvector centrality gives greater weight to a node the more
> # it is connected to other highly connected nodes. A node
> # connected to five high-scoring nodes will have higher
> # eigenvector centrality than a node connected to five low-scoring
> # nodes. Thus, it is often interpreted as measuring a node’s
> # network importance.
> #
> # In directed networks, there are ’In’ and ’Out’ versions. In
> # information flow studies, for instance, In-Eigenvector scores
> # would reflect which nodes are high on receiving information,
> # while Out-Eigenvector scores would reflect which nodes are high
> # on broadcasting information.
> #
> # For these data, we will simply symmetrize to generate an
> # undirected eigenvector centrality score.
> #
> # Note that, unlike the other centrality measures, evcent()
> # returns a complex object rather than a simple vector. Thus,
> # we need to first get the evcent() output and then select the
> # eigenvector scores from it.
> s641_social_undirected <- as.undirected(s641_social, mode=’collapse’)
> ev_obj_social <- evcent(s641_social_undirected)
> eigen_social <- ev_obj_social$vector > eigen_social [1] 2.418251e-01 1.735366e-01 -1.190031e-17 2.418251e-01 1.004841e-01 [6] 1.530350e-02 -1.190031e-17 2.004592e-02 7.671178e-02 1.807292e-01 [11] 3.692292e-01 3.605430e-02 7.741214e-01 7.027272e-01 1.000000e+00 [16] 9.385917e-01 5.482951e-01 8.098439e-01 8.698860e-01 > > ##### > # Extra Credit - what code would you write in R > # to get the directed versions of eigenvector centrality? > ##### > > # To get the summary table, we’ll construct a data frame with > # the vertices as rows and the centrality scores as columns. > # > # Note that the vertex IDs are NOT the same as the first column > # of row numbers. This is because we previously removed isolates. > central_social <- data.frame(V(s641_social)$name, indegree_social, outdegree_social, incloseness_social, outcloseness_social, betweenness_social, eigen_social)
> central_social
V.s641_social..name indegree_social outdegree_social incloseness_social
1                    1               3                3         0.16363636
2                    2               1                1         0.15652174
3                    4               1                1         0.05555556
4                    5               3                3         0.16363636
5                    6               3                3         0.15000000
6                    7               1                1         0.13533835
7                    8               1                1         0.05555556
8                    9               1                1         0.13533835
9                   10               2                2         0.15000000
10                  11               2                1         0.22500000
11                  12               3                3         0.16513761
12                  15               1                1         0.18947368
13                  16               5                5         0.17475728
14                  17               4                4         0.16216216
15                  18               7                6         0.17821782
16                  19               5                6         0.17142857
17                  20               3                3         0.16071429
18                  21               5                4         0.17142857
19                  22               6                8         0.17647059
outcloseness_social betweenness_social  eigen_social
1           0.23684211         24.0000000  2.418251e-01
2           0.22222222          0.0000000  1.735366e-01
3           0.05555556          0.0000000 -1.190031e-17
4           0.23684211         24.0000000  2.418251e-01
5           0.20454545         28.0000000  1.004841e-01
6           0.16981132          0.0000000  1.530350e-02
7           0.05555556          0.0000000 -1.190031e-17
8           0.17475728          0.0000000  2.004592e-02
9           0.19780220         28.0000000  7.671178e-02
10          0.05555556         15.0000000  1.807292e-01
11          0.23076923         52.0000000  3.692292e-01
12          0.05555556          0.0000000  3.605430e-02
13          0.25714286         45.8333333  7.741214e-01
14          0.22500000          0.8333333  7.027272e-01
15          0.23684211         33.0000000  1.000000e+00
16          0.25352113         14.7500000  9.385917e-01
17          0.22222222          0.2500000  5.482951e-01
18          0.24657534         13.5000000  8.098439e-01
19          0.27272727        126.8333333  8.698860e-01
>
> # Now we’ll examine the table to find the most central actors
> # according to the different measures we have. When looking at
> # each of these measures, it’s a good idea to have your plot on
> # hand so you can sanity-check the results.
> plot(s641_social, vertex.size=10, vertex.label=V(s641_social)$name, + edge.arrow.size = 0.5, layout=layout.fruchterman.reingold,main=’Classroom S641 Social Talk’) > > # Show table sorted by decreasing indegree. The order() function > # returns a vector in ascending order; the minus sign flips it > # to be descending order. Top actors are 18, 22 and 16. > central_social[order(-central_social$indegree_social),]
V.s641_social..name indegree_social outdegree_social incloseness_social
15                  18               7                6         0.17821782
19                  22               6                8         0.17647059
13                  16               5                5         0.17475728
16                  19               5                6         0.17142857
18                  21               5                4         0.17142857
14                  17               4                4         0.16216216
1                    1               3                3         0.16363636
4                    5               3                3         0.16363636
5                    6               3                3         0.15000000
11                  12               3                3         0.16513761
17                  20               3                3         0.16071429
9                   10               2                2         0.15000000
10                  11               2                1         0.22500000
2                    2               1                1         0.15652174
3                    4               1                1         0.05555556
6                    7               1                1         0.13533835
7                    8               1                1         0.05555556
8                    9               1                1         0.13533835
12                  15               1                1         0.18947368
outcloseness_social betweenness_social  eigen_social
15          0.23684211         33.0000000  1.000000e+00
19          0.27272727        126.8333333  8.698860e-01
13          0.25714286         45.8333333  7.741214e-01
16          0.25352113         14.7500000  9.385917e-01
18          0.24657534         13.5000000  8.098439e-01
14          0.22500000          0.8333333  7.027272e-01
1           0.23684211         24.0000000  2.418251e-01
4           0.23684211         24.0000000  2.418251e-01
5           0.20454545         28.0000000  1.004841e-01
11          0.23076923         52.0000000  3.692292e-01
17          0.22222222          0.2500000  5.482951e-01
9           0.19780220         28.0000000  7.671178e-02
10          0.05555556         15.0000000  1.807292e-01
2           0.22222222          0.0000000  1.735366e-01
3           0.05555556          0.0000000 -1.190031e-17
6           0.16981132          0.0000000  1.530350e-02
7           0.05555556          0.0000000 -1.190031e-17
8           0.17475728          0.0000000  2.004592e-02
12          0.05555556          0.0000000  3.605430e-02
>
> # Outdegree: 22, 18 and 19.
> central_social[order(-central_social$outdegree_social),] V.s641_social..name indegree_social outdegree_social incloseness_social 19 22 6 8 0.17647059 15 18 7 6 0.17821782 16 19 5 6 0.17142857 13 16 5 5 0.17475728 14 17 4 4 0.16216216 18 21 5 4 0.17142857 1 1 3 3 0.16363636 4 5 3 3 0.16363636 5 6 3 3 0.15000000 11 12 3 3 0.16513761 17 20 3 3 0.16071429 9 10 2 2 0.15000000 2 2 1 1 0.15652174 3 4 1 1 0.05555556 6 7 1 1 0.13533835 7 8 1 1 0.05555556 8 9 1 1 0.13533835 10 11 2 1 0.22500000 12 15 1 1 0.18947368 outcloseness_social betweenness_social eigen_social 19 0.27272727 126.8333333 8.698860e-01 15 0.23684211 33.0000000 1.000000e+00 16 0.25352113 14.7500000 9.385917e-01 13 0.25714286 45.8333333 7.741214e-01 14 0.22500000 0.8333333 7.027272e-01 18 0.24657534 13.5000000 8.098439e-01 1 0.23684211 24.0000000 2.418251e-01 4 0.23684211 24.0000000 2.418251e-01 5 0.20454545 28.0000000 1.004841e-01 11 0.23076923 52.0000000 3.692292e-01 17 0.22222222 0.2500000 5.482951e-01 9 0.19780220 28.0000000 7.671178e-02 2 0.22222222 0.0000000 1.735366e-01 3 0.05555556 0.0000000 -1.190031e-17 6 0.16981132 0.0000000 1.530350e-02 7 0.05555556 0.0000000 -1.190031e-17 8 0.17475728 0.0000000 2.004592e-02 10 0.05555556 15.0000000 1.807292e-01 12 0.05555556 0.0000000 3.605430e-02 > > # In-closeness: 11, 15 and 18. > # NOTE: For some reason, this operation returns strange values; > # a visual inspection of the plot suggests that 11, 15, and 18 > # are not central actors at all. This could be a bug. > central_social[order(-central_social$incloseness_social),]
V.s641_social..name indegree_social outdegree_social incloseness_social
10                  11               2                1         0.22500000
12                  15               1                1         0.18947368
15                  18               7                6         0.17821782
19                  22               6                8         0.17647059
13                  16               5                5         0.17475728
16                  19               5                6         0.17142857
18                  21               5                4         0.17142857
11                  12               3                3         0.16513761
1                    1               3                3         0.16363636
4                    5               3                3         0.16363636
14                  17               4                4         0.16216216
17                  20               3                3         0.16071429
2                    2               1                1         0.15652174
5                    6               3                3         0.15000000
9                   10               2                2         0.15000000
6                    7               1                1         0.13533835
8                    9               1                1         0.13533835
3                    4               1                1         0.05555556
7                    8               1                1         0.05555556
outcloseness_social betweenness_social  eigen_social
10          0.05555556         15.0000000  1.807292e-01
12          0.05555556          0.0000000  3.605430e-02
15          0.23684211         33.0000000  1.000000e+00
19          0.27272727        126.8333333  8.698860e-01
13          0.25714286         45.8333333  7.741214e-01
16          0.25352113         14.7500000  9.385917e-01
18          0.24657534         13.5000000  8.098439e-01
11          0.23076923         52.0000000  3.692292e-01
1           0.23684211         24.0000000  2.418251e-01
4           0.23684211         24.0000000  2.418251e-01
14          0.22500000          0.8333333  7.027272e-01
17          0.22222222          0.2500000  5.482951e-01
2           0.22222222          0.0000000  1.735366e-01
5           0.20454545         28.0000000  1.004841e-01
9           0.19780220         28.0000000  7.671178e-02
6           0.16981132          0.0000000  1.530350e-02
8           0.17475728          0.0000000  2.004592e-02
3           0.05555556          0.0000000 -1.190031e-17
7           0.05555556          0.0000000 -1.190031e-17
>
> # Out-closeness: 22, 16, and 19
> central_social[order(-central_social$outcloseness_social),] V.s641_social..name indegree_social outdegree_social incloseness_social 19 22 6 8 0.17647059 13 16 5 5 0.17475728 16 19 5 6 0.17142857 18 21 5 4 0.17142857 1 1 3 3 0.16363636 4 5 3 3 0.16363636 15 18 7 6 0.17821782 11 12 3 3 0.16513761 14 17 4 4 0.16216216 2 2 1 1 0.15652174 17 20 3 3 0.16071429 5 6 3 3 0.15000000 9 10 2 2 0.15000000 8 9 1 1 0.13533835 6 7 1 1 0.13533835 3 4 1 1 0.05555556 7 8 1 1 0.05555556 10 11 2 1 0.22500000 12 15 1 1 0.18947368 outcloseness_social betweenness_social eigen_social 19 0.27272727 126.8333333 8.698860e-01 13 0.25714286 45.8333333 7.741214e-01 16 0.25352113 14.7500000 9.385917e-01 18 0.24657534 13.5000000 8.098439e-01 1 0.23684211 24.0000000 2.418251e-01 4 0.23684211 24.0000000 2.418251e-01 15 0.23684211 33.0000000 1.000000e+00 11 0.23076923 52.0000000 3.692292e-01 14 0.22500000 0.8333333 7.027272e-01 2 0.22222222 0.0000000 1.735366e-01 17 0.22222222 0.2500000 5.482951e-01 5 0.20454545 28.0000000 1.004841e-01 9 0.19780220 28.0000000 7.671178e-02 8 0.17475728 0.0000000 2.004592e-02 6 0.16981132 0.0000000 1.530350e-02 3 0.05555556 0.0000000 -1.190031e-17 7 0.05555556 0.0000000 -1.190031e-17 10 0.05555556 15.0000000 1.807292e-01 12 0.05555556 0.0000000 3.605430e-02 > > # Eigenvector: 18, 19, and 16 > central_social[order(-central_social$eigen_social),]
V.s641_social..name indegree_social outdegree_social incloseness_social
15                  18               7                6         0.17821782
16                  19               5                6         0.17142857
19                  22               6                8         0.17647059
18                  21               5                4         0.17142857
13                  16               5                5         0.17475728
14                  17               4                4         0.16216216
17                  20               3                3         0.16071429
11                  12               3                3         0.16513761
1                    1               3                3         0.16363636
4                    5               3                3         0.16363636
10                  11               2                1         0.22500000
2                    2               1                1         0.15652174
5                    6               3                3         0.15000000
9                   10               2                2         0.15000000
12                  15               1                1         0.18947368
8                    9               1                1         0.13533835
6                    7               1                1         0.13533835
3                    4               1                1         0.05555556
7                    8               1                1         0.05555556
outcloseness_social betweenness_social  eigen_social
15          0.23684211         33.0000000  1.000000e+00
16          0.25352113         14.7500000  9.385917e-01
19          0.27272727        126.8333333  8.698860e-01
18          0.24657534         13.5000000  8.098439e-01
13          0.25714286         45.8333333  7.741214e-01
14          0.22500000          0.8333333  7.027272e-01
17          0.22222222          0.2500000  5.482951e-01
11          0.23076923         52.0000000  3.692292e-01
1           0.23684211         24.0000000  2.418251e-01
4           0.23684211         24.0000000  2.418251e-01
10          0.05555556         15.0000000  1.807292e-01
2           0.22222222          0.0000000  1.735366e-01
5           0.20454545         28.0000000  1.004841e-01
9           0.19780220         28.0000000  7.671178e-02
12          0.05555556          0.0000000  3.605430e-02
8           0.17475728          0.0000000  2.004592e-02
6           0.16981132          0.0000000  1.530350e-02
3           0.05555556          0.0000000 -1.190031e-17
7           0.05555556          0.0000000 -1.190031e-17
>
> # let’s make a plot or two with these summary statistics
>
> # To visualize these data, we can create a barplot for each
> # centrality measure. In all cases, the y-axis is the value of
> # each category and the x-axis is the node number.
> barplot(central_social$indegree_social, names.arg=central_social$V.s641_social..name)
> barplot(central_social$outdegree_social, names.arg=central_social$V.s641_social..name)
> barplot(central_social$incloseness_social, names.arg=central_social$V.s641_social..name)
> barplot(central_social$outcloseness_social, names.arg=central_social$V.s641_social..name)
> barplot(central_social$betweenness_social, names.arg=central_social$V.s641_social..name)
> barplot(central_social$eigen_social, names.arg=central_social$V.s641_social..name)
>
> # Question #2 - What can we say about the social actors if we compare the bar plots?
> # Who seems to run the show in sociable affairs? Who seems to bridge sociable conversations?
>
> ###
> # 4. CORRELATIONS BETWEEN CENTRALITY MEASURES
> ###
>
> # Now we’ll compute correlations betwee the columns to determine
> # how closely these measures of centrality are interrelated.
>
> # Generate a table of pairwise correlations.
> cor(central_social[,2:7])
indegree_social outdegree_social incloseness_social
indegree_social           1.0000000        0.9482820          0.4474301
outdegree_social          0.9482820        1.0000000          0.3718385
incloseness_social        0.4474301        0.3718385          1.0000000
outcloseness_social       0.6939672        0.7201862          0.3865818
betweenness_social        0.5991529        0.7242923          0.3040817
eigen_social              0.9429737        0.9047671          0.4440923
outcloseness_social betweenness_social eigen_social
indegree_social               0.6939672          0.5991529    0.9429737
outdegree_social              0.7201862          0.7242923    0.9047671
incloseness_social            0.3865818          0.3040817    0.4440923
outcloseness_social           1.0000000          0.4781439    0.6753520
betweenness_social            0.4781439          1.0000000    0.4586893
eigen_social                  0.6753520          0.4586893    1.0000000
>
> # INTERPRETATION:
> #
> # Indegree and outdegree are very closely correlated (rho = 0.95),
> # indicating that social talk with others is reciprocated (i.e.,
> # if you talk to others, they tend to talk back to you).
> #
> # The same is not true of incloseness and outcloseness (rho =
> # 0.38), indicating that the closeness calculated from inbound
> # paths is not strongly associated with with closeness from
> # outbound paths.
> #
> # In- and out-degree are highly correlated with eigenvector
> # centrality, indicating that the students that talk the most to
> # others (or, relatedly, are talked to the most by others) are
> # also the ones that are connected to other highly connected
> # students -- possibly indicating high density cliques around
> # these individuals.
> #
> # Betweennes shows the highest corelation with outdegree, follwed
> # by indegree. In the case of this particular network, it seems
> # that the individuals that talk to the most others are the
> # likeliest to serve as bridges between the particular cliques
> # (see, e.g., 22 in the plot).
>
>
> ###
> # 5. REPEAT FOR TASK TALK
> ###
>
> # Indegree
> # We should have 20 entries, indicating 2 isolates.
[1]  1  1  1  1  1  1  1  1  1  1  2  1  1  2  3  4  3  2  3 17
>
> # Outdegree
[1]  1  1  1  1  1  1  1  1  1  1  2  1  1  2  3  4  3  2  3 17
>
> # In-closeness
[1] 0.26027397 0.26027397 0.05263158 0.26027397 0.26027397 0.26027397
[7] 0.05263158 0.26027397 0.26027397 0.26027397 0.26388889 0.26027397
[13] 0.26027397 0.26388889 0.26760563 0.27142857 0.26760563 0.26388889
[19] 0.26760563 0.33333333
>
> # Out-closeness
[1] 0.26027397 0.26027397 0.05263158 0.26027397 0.26027397 0.26027397
[7] 0.05263158 0.26027397 0.26027397 0.26027397 0.26388889 0.26027397
[13] 0.26027397 0.26388889 0.26760563 0.27142857 0.26760563 0.26388889
[19] 0.26760563 0.33333333
>
> # Betweenness. Note that the closeness measures arent very high
> # for node 22, but the betweenness is off the charts.
[1]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   2   1   0   0
[20] 257
>
> # Eigenvector
> eigen_task <-ev_obj_task$vector > eigen_task [1] 2.154856e-01 2.154856e-01 1.667947e-17 2.154856e-01 2.154856e-01 [6] 2.154856e-01 1.667947e-17 2.154856e-01 2.154856e-01 2.154856e-01 [11] 3.136051e-01 2.154856e-01 2.154856e-01 2.887339e-01 3.997443e-01 [16] 4.553413e-01 3.399216e-01 2.887339e-01 3.997443e-01 1.000000e+00 > > # Generate a data frame with all centrality values > central_task <- data.frame(V(s641_task)$name, indegree_task, outdegree_task, incloseness_task, outcloseness_task, betweenness_task, eigen_task)
1                  1             1              1       0.26027397
2                  2             1              1       0.26027397
3                  4             1              1       0.05263158
4                  5             1              1       0.26027397
5                  6             1              1       0.26027397
6                  7             1              1       0.26027397
7                  8             1              1       0.05263158
8                  9             1              1       0.26027397
9                 10             1              1       0.26027397
10                11             1              1       0.26027397
11                13             2              2       0.26388889
12                14             1              1       0.26027397
13                15             1              1       0.26027397
14                16             2              2       0.26388889
15                17             3              3       0.26760563
16                18             4              4       0.27142857
17                19             3              3       0.26760563
18                20             2              2       0.26388889
19                21             3              3       0.26760563
20                22            17             17       0.33333333
1         0.26027397                0 2.154856e-01
2         0.26027397                0 2.154856e-01
3         0.05263158                0 1.667947e-17
4         0.26027397                0 2.154856e-01
5         0.26027397                0 2.154856e-01
6         0.26027397                0 2.154856e-01
7         0.05263158                0 1.667947e-17
8         0.26027397                0 2.154856e-01
9         0.26027397                0 2.154856e-01
10        0.26027397                0 2.154856e-01
11        0.26388889                0 3.136051e-01
12        0.26027397                0 2.154856e-01
13        0.26027397                0 2.154856e-01
14        0.26388889                0 2.887339e-01
15        0.26760563                0 3.997443e-01
16        0.27142857                2 4.553413e-01
17        0.26760563                1 3.399216e-01
18        0.26388889                0 2.887339e-01
19        0.26760563                0 3.997443e-01
20        0.33333333              257 1.000000e+00
>
> # In-degree: 22, 18 and 17
> central_task[order(-central_task$indegree_task),] V.s641_task..name indegree_task outdegree_task incloseness_task 20 22 17 17 0.33333333 16 18 4 4 0.27142857 15 17 3 3 0.26760563 17 19 3 3 0.26760563 19 21 3 3 0.26760563 11 13 2 2 0.26388889 14 16 2 2 0.26388889 18 20 2 2 0.26388889 1 1 1 1 0.26027397 2 2 1 1 0.26027397 3 4 1 1 0.05263158 4 5 1 1 0.26027397 5 6 1 1 0.26027397 6 7 1 1 0.26027397 7 8 1 1 0.05263158 8 9 1 1 0.26027397 9 10 1 1 0.26027397 10 11 1 1 0.26027397 12 14 1 1 0.26027397 13 15 1 1 0.26027397 outcloseness_task betweenness_task eigen_task 20 0.33333333 257 1.000000e+00 16 0.27142857 2 4.553413e-01 15 0.26760563 0 3.997443e-01 17 0.26760563 1 3.399216e-01 19 0.26760563 0 3.997443e-01 11 0.26388889 0 3.136051e-01 14 0.26388889 0 2.887339e-01 18 0.26388889 0 2.887339e-01 1 0.26027397 0 2.154856e-01 2 0.26027397 0 2.154856e-01 3 0.05263158 0 1.667947e-17 4 0.26027397 0 2.154856e-01 5 0.26027397 0 2.154856e-01 6 0.26027397 0 2.154856e-01 7 0.05263158 0 1.667947e-17 8 0.26027397 0 2.154856e-01 9 0.26027397 0 2.154856e-01 10 0.26027397 0 2.154856e-01 12 0.26027397 0 2.154856e-01 13 0.26027397 0 2.154856e-01 > > # Outdegree: 22, 18 and 17 > central_task[order(-central_task$outdegree_task),]
20                22            17             17       0.33333333
16                18             4              4       0.27142857
15                17             3              3       0.26760563
17                19             3              3       0.26760563
19                21             3              3       0.26760563
11                13             2              2       0.26388889
14                16             2              2       0.26388889
18                20             2              2       0.26388889
1                  1             1              1       0.26027397
2                  2             1              1       0.26027397
3                  4             1              1       0.05263158
4                  5             1              1       0.26027397
5                  6             1              1       0.26027397
6                  7             1              1       0.26027397
7                  8             1              1       0.05263158
8                  9             1              1       0.26027397
9                 10             1              1       0.26027397
10                11             1              1       0.26027397
12                14             1              1       0.26027397
13                15             1              1       0.26027397
20        0.33333333              257 1.000000e+00
16        0.27142857                2 4.553413e-01
15        0.26760563                0 3.997443e-01
17        0.26760563                1 3.399216e-01
19        0.26760563                0 3.997443e-01
11        0.26388889                0 3.136051e-01
14        0.26388889                0 2.887339e-01
18        0.26388889                0 2.887339e-01
1         0.26027397                0 2.154856e-01
2         0.26027397                0 2.154856e-01
3         0.05263158                0 1.667947e-17
4         0.26027397                0 2.154856e-01
5         0.26027397                0 2.154856e-01
6         0.26027397                0 2.154856e-01
7         0.05263158                0 1.667947e-17
8         0.26027397                0 2.154856e-01
9         0.26027397                0 2.154856e-01
10        0.26027397                0 2.154856e-01
12        0.26027397                0 2.154856e-01
13        0.26027397                0 2.154856e-01
>
> # Incloseness: 22, 18 and 17
> central_task[order(-central_task$incloseness_task),] V.s641_task..name indegree_task outdegree_task incloseness_task 20 22 17 17 0.33333333 16 18 4 4 0.27142857 15 17 3 3 0.26760563 17 19 3 3 0.26760563 19 21 3 3 0.26760563 11 13 2 2 0.26388889 14 16 2 2 0.26388889 18 20 2 2 0.26388889 1 1 1 1 0.26027397 2 2 1 1 0.26027397 4 5 1 1 0.26027397 5 6 1 1 0.26027397 6 7 1 1 0.26027397 8 9 1 1 0.26027397 9 10 1 1 0.26027397 10 11 1 1 0.26027397 12 14 1 1 0.26027397 13 15 1 1 0.26027397 3 4 1 1 0.05263158 7 8 1 1 0.05263158 outcloseness_task betweenness_task eigen_task 20 0.33333333 257 1.000000e+00 16 0.27142857 2 4.553413e-01 15 0.26760563 0 3.997443e-01 17 0.26760563 1 3.399216e-01 19 0.26760563 0 3.997443e-01 11 0.26388889 0 3.136051e-01 14 0.26388889 0 2.887339e-01 18 0.26388889 0 2.887339e-01 1 0.26027397 0 2.154856e-01 2 0.26027397 0 2.154856e-01 4 0.26027397 0 2.154856e-01 5 0.26027397 0 2.154856e-01 6 0.26027397 0 2.154856e-01 8 0.26027397 0 2.154856e-01 9 0.26027397 0 2.154856e-01 10 0.26027397 0 2.154856e-01 12 0.26027397 0 2.154856e-01 13 0.26027397 0 2.154856e-01 3 0.05263158 0 1.667947e-17 7 0.05263158 0 1.667947e-17 > > # Outcloseness: 22, 18 and 17 > central_task[order(-central_task$outcloseness_task),]
20                22            17             17       0.33333333
16                18             4              4       0.27142857
15                17             3              3       0.26760563
17                19             3              3       0.26760563
19                21             3              3       0.26760563
11                13             2              2       0.26388889
14                16             2              2       0.26388889
18                20             2              2       0.26388889
1                  1             1              1       0.26027397
2                  2             1              1       0.26027397
4                  5             1              1       0.26027397
5                  6             1              1       0.26027397
6                  7             1              1       0.26027397
8                  9             1              1       0.26027397
9                 10             1              1       0.26027397
10                11             1              1       0.26027397
12                14             1              1       0.26027397
13                15             1              1       0.26027397
3                  4             1              1       0.05263158
7                  8             1              1       0.05263158
20        0.33333333              257 1.000000e+00
16        0.27142857                2 4.553413e-01
15        0.26760563                0 3.997443e-01
17        0.26760563                1 3.399216e-01
19        0.26760563                0 3.997443e-01
11        0.26388889                0 3.136051e-01
14        0.26388889                0 2.887339e-01
18        0.26388889                0 2.887339e-01
1         0.26027397                0 2.154856e-01
2         0.26027397                0 2.154856e-01
4         0.26027397                0 2.154856e-01
5         0.26027397                0 2.154856e-01
6         0.26027397                0 2.154856e-01
8         0.26027397                0 2.154856e-01
9         0.26027397                0 2.154856e-01
10        0.26027397                0 2.154856e-01
12        0.26027397                0 2.154856e-01
13        0.26027397                0 2.154856e-01
3         0.05263158                0 1.667947e-17
7         0.05263158                0 1.667947e-17
>
> # Eigenvector: 22, 18 and 17
> central_task[order(-central_task$eigen_task),] V.s641_task..name indegree_task outdegree_task incloseness_task 20 22 17 17 0.33333333 16 18 4 4 0.27142857 15 17 3 3 0.26760563 19 21 3 3 0.26760563 17 19 3 3 0.26760563 11 13 2 2 0.26388889 14 16 2 2 0.26388889 18 20 2 2 0.26388889 1 1 1 1 0.26027397 2 2 1 1 0.26027397 4 5 1 1 0.26027397 5 6 1 1 0.26027397 6 7 1 1 0.26027397 8 9 1 1 0.26027397 9 10 1 1 0.26027397 10 11 1 1 0.26027397 12 14 1 1 0.26027397 13 15 1 1 0.26027397 3 4 1 1 0.05263158 7 8 1 1 0.05263158 outcloseness_task betweenness_task eigen_task 20 0.33333333 257 1.000000e+00 16 0.27142857 2 4.553413e-01 15 0.26760563 0 3.997443e-01 19 0.26760563 0 3.997443e-01 17 0.26760563 1 3.399216e-01 11 0.26388889 0 3.136051e-01 14 0.26388889 0 2.887339e-01 18 0.26388889 0 2.887339e-01 1 0.26027397 0 2.154856e-01 2 0.26027397 0 2.154856e-01 4 0.26027397 0 2.154856e-01 5 0.26027397 0 2.154856e-01 6 0.26027397 0 2.154856e-01 8 0.26027397 0 2.154856e-01 9 0.26027397 0 2.154856e-01 10 0.26027397 0 2.154856e-01 12 0.26027397 0 2.154856e-01 13 0.26027397 0 2.154856e-01 3 0.05263158 0 1.667947e-17 7 0.05263158 0 1.667947e-17 > > # Look at barplots > barplot(central_task$indegree_task, names.arg=central_task$V.s641_task..name) > barplot(central_task$outdegree_task, names.arg=central_task$V.s641_task..name) > barplot(central_task$incloseness_task, names.arg=central_task$V.s641_task..name) > barplot(central_task$outcloseness_task, names.arg=central_task$V.s641_task..name) > barplot(central_task$betweenness_task, names.arg=central_task$V.s641_task..name) > barplot(central_task$eigen_task, names.arg=central_task$V.s641_task..name) > > # Question #3 - What can we say about the social actors if we compare the bar plots? > # Who seems to run the show in task affairs? Who seems to bridge task conversations? > > ### > # 6. TASK/SOCIAL CORRELATIONS > ### > > # Note that in order to do this, we need to either have no missing > # data or use pairwise complete observations. > # > # It would be nice if the centrality functions padded N/A or zero > # data for the isolates, because then the dimensions of the two > # matrices would be compatible. But right now we have 19 nodes for > # social interaction and 20 nodes for task interaction. So first > # we have to do some hacky R stuff to make them both have 22 > # nodes. > > # First, we’ll extract the node names from the SSL data, using > # levels() because it’s a factor and converting it to numbers so > # we can match with the TSL data. Then we’ll repeat for TSL. > connectednodes_social = as.numeric(levels(central_social$V.s641_social..name))[central_social$V.s641_social..name] > connectednodes_task = as.numeric(levels(central_task$V.s641_task..name))[central_task\$V.s641_task..name]
>
> # Check that we did this correctly: SSL should have 19 nodes, and
> # TSL should have 20 nodes.
> length(connectednodes_social)
[1] 19
[1] 20
>
> # Extract matches for each data set, take that subset and use
> # columns 2 through 7 to create the correlation matrix. This
> # computes the correlations based only on the actors in both
> # graphs (18 in total).
indegree_social         0.5827715      0.5827715        0.4828844
outdegree_social        0.7405082      0.7405082        0.4892710
incloseness_social      0.2062057      0.2062057        0.8645480
outcloseness_social     0.3931247      0.3931247        0.6730453
betweenness_social      0.8804683      0.8804683        0.4325887
eigen_social            0.5489725      0.5489725        0.4637872
indegree_social             0.4828844        0.3911312  0.7271716
outdegree_social            0.4892710        0.5870139  0.8218924
incloseness_social          0.8645480        0.1366851  0.4983746
outcloseness_social         0.6730453        0.2766534  0.6018555
betweenness_social          0.4325887        0.8824737  0.8259574
eigen_social                0.4637872        0.3365687  0.7036670
>
>
> # INTERPRETATION:
> #
> # eigen_task is correlated with betweenness_social (rho=0.83) and
> # outdegree (rho=0.82), possibly because those who are
> # important in talk on tasks also serve as bridges for talk on
> # social issues and have many outbound ties.
> #
> # indegree_task and betweenness_social (rho=0.88), and
> # outdegree_task and betweenness_social (rho=0.88) are correlated,
> # possibly because the number of indegree and outdegree ties a
> # node has with respect to task talk, the more they serve as a
> # bridge on social talk.
> #
> # incloseness_task and incloseness_social (rho=0.86) are
> # correlated, meaning that those who serve in shortest parths past
> # on inbound ties are equivalent for both social talk and task
> # talk, which seems to make sense given the betweenness
> # correlations with network importance and degree between task and
> # social talk more interpretations are possible as well.
>
> # Question #4 - What can we infer about s641 from these results?
> # What sort of substantive story can we derive from it?