Description Usage Arguments Details Value Author(s) References See Also Examples
Performs the brokerage analysis of Gould and Fernandez on one or more input graphs, given a class membership vector.
1  brokerage(g, cl)

g 
one or more input graphs. 
cl 
a vector of class memberships. 
Gould and Fernandez (following Marsden and others) describe brokerage as the role played by a social actor who mediates contact between two alters. More formally, vertex v is a broker for distinct vertices a and b iff a > v > b and a !> b. Where actors belong to a priori distinct groups, group membership may be used to segment brokerage roles into particular types. Let A > B > C denote the twopath associated with a brokerage structure, such that some vertex from group B brokers the connection from some vertex from group A to a vertex in group C. The types of brokerage roles defined by Gould and Fernandez (and their accompanying twopath structures) are then defined in terms of group membership as follows:
w_I: Coordinator role; the broker mediates contact between two individuals from his or her own group. Twopath structure: A > A > A
w_O: Itinerant broker role; the broker mediates contact between two individuals from a single group to which he or she does not belong. Twopath structure: A > B > A
b_{IO}: Representative role; the broker mediates an incoming contact from an outgroup member to an ingroup member. Twopath structure: A > B > B
b_{OI}: Gatekeeper role; the broker mediates an outgoing contact from an ingroup member to an outgroup member. Twopath structure: A > A > B
b_O: Liaison role; the broker mediates contact between two individuals from different groups, neither of which is the group to which he or she belongs. Twopath structure: A > B > C
t: Total (cumulative) brokerage role occupancy. (Any of the above twopaths.)
The brokerage score for a given vertex with respect to a given role is the number of ordered pairs having the appropriate group membership(s) brokered by said vertex. brokerage
computes the brokerage scores for each vertex, given an input graph and vector of class memberships. Aggregate scores are also computed at the graph level, which correspond to the total frequency of each role type within the network structure. Expectations and variances of the brokerage scores conditional on size and density are computed, along with approximate ztests for incidence of brokerage. (Note that the accuracy of the normality assumption is not known in the general case; see Gould and Fernandez (1989) for details. Simulationbased tests may be desirable as an alternative.)
An object of class brokerage
, containing the following elements:
raw.nli 
The matrix of observed brokerage scores, by vertex 
exp.nli 
The matrix of expected brokerage scores, by vertex 
sd.nli 
The matrix of predicted brokerage score standard deviations, by vertex 
z.nli 
The matrix of standardized brokerage scores, by vertex 
raw.gli 
The vector of observed aggregate brokerage scores 
exp.gli 
The vector of expected aggregate brokerage scores 
sd.gli 
The vector of predicted aggregate brokerage score standard deviations 
z.gli 
The vector of standardized aggregate brokerage scores 
exp.grp 
The matrix of expected brokerage scores, by group 
sd.grp 
The matrix of predicted brokerage score standard deviations, by group 
cl 
The vector of class memberships 
clid 
The original class names 
n 
The input class sizes 
N 
The order of the input network 
Carter T. Butts buttsc@uci.edu
Gould, R.V. and Fernandez, R.M. 1989. “Structures of Mediation: A Formal Approach to Brokerage in Transaction Networks.” Sociological Methodology, 19: 89126.
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Loading required package: statnet.common
Loading required package: network
network: Classes for Relational Data
Version 1.13.0 created on 20150831.
copyright (c) 2005, Carter T. Butts, University of CaliforniaIrvine
Mark S. Handcock, University of California  Los Angeles
David R. Hunter, Penn State University
Martina Morris, University of Washington
Skye BenderdeMoll, University of Washington
For citation information, type citation("network").
Type help("networkpackage") to get started.
sna: Tools for Social Network Analysis
Version 2.4 created on 20160723.
copyright (c) 2005, Carter T. Butts, University of CaliforniaIrvine
For citation information, type citation("sna").
Type help(package="sna") to get started.
GouldFernandez Brokerage Analysis
Global Brokerage Properties
t E(t) Sd(t) z Pr(>z)
w_I 22.0000 22.7122 5.5569 0.1282 0.8980
w_O 93.0000 75.7074 16.8818 1.0243 0.3057
b_IO 81.0000 75.7074 14.4164 0.3671 0.7135
b_OI 80.0000 75.7074 14.4164 0.2978 0.7659
b_O 95.0000 94.6343 11.2836 0.0324 0.9741
t 371.0000 344.4688 29.6401 0.8951 0.3707
Individual Properties (by Group)
Group ID: 1
w_I w_O b_IO b_OI b_O t w_I w_O b_IO b_OI
[1,] 2 6 5 7 6 26 0.3374547 0.3335747 0.0136666 0.5659030
[2,] 2 6 5 4 5 22 0.3374547 0.3335747 0.0136666 0.3034514
[3,] 0 7 0 9 5 21 1.0516718 0.6836598 1.4625905 1.1454725
[4,] 2 4 7 7 8 28 0.3374547 0.3665956 0.5659030 0.5659030
[5,] 1 6 10 2 5 24 0.3571086 0.3335747 1.4352573 0.8830210
b_O t
[1,] 0.09008752 0.3230293
[2,] 0.38167864 0.1026511
[3,] 0.38167864 0.2090712
[4,] 0.49309473 0.5358695
[5,] 0.38167864 0.1101891
Group ID: 2
w_I w_O b_IO b_OI b_O t w_I w_O b_IO b_OI
[1,] 2 7 10 6 10 35 0.3374547 0.6836598 1.4352573 0.2761182
[2,] 4 2 8 3 3 20 1.7265813 1.0667659 0.8556878 0.5932362
[3,] 1 7 3 9 6 26 0.3571086 0.6836598 0.5932362 1.1454725
[4,] 1 8 10 3 9 31 0.3571086 1.0337450 1.4352573 0.5932362
[5,] 3 9 8 14 7 41 1.0320180 1.3838301 0.8556878 2.5943965
b_O t
[1,] 1.07627698 1.2808102
[2,] 0.96486089 0.3154913
[3,] 0.09008752 0.3230293
[4,] 0.78468585 0.8551298
[5,] 0.20150360 1.9193309
Group ID: 3
w_I w_O b_IO b_OI b_O t w_I w_O b_IO b_OI
[1,] 1 3 4 4 3 15 0.3571086 0.71668073 0.3034514 0.3034514
[2,] 1 11 3 7 11 33 0.3571086 2.08400043 0.5932362 0.5659030
[3,] 1 9 3 3 8 24 0.3571086 1.38383014 0.5932362 0.5932362
[4,] 0 5 0 1 3 9 1.0516718 0.01651044 1.4625905 1.1728057
[5,] 1 3 5 1 6 16 0.3571086 0.71668073 0.0136666 1.1728057
b_O t
[1,] 0.96486089 0.8475918
[2,] 1.36786810 1.0679700
[3,] 0.49309473 0.1101891
[4,] 0.96486089 1.4861124
[5,] 0.09008752 0.7411717
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