Analyzed organizational network resulting in improved communication, reduced hierarchy and better collaboration

1. 1
NETWORK
ORGANIZATION
Anvit Goyal

2. 2
Tableof Contents
Data...........................................................................................................................................................................3
Analysis.....................................................................................................................................................................3
Conclusion ................................................................................................................................................................3
Appendix 1: Survey ..................................................................................................................................................5
Appendix 2: Age vs Degree Centrality...................................................................................................................13
Appendix 3: Tenure vs Degree Centrality .............................................................................................................15
Appendix 4: Department vs Degree Centrality.....................................................................................................17
Appendix 5: Summary of model 1.........................................................................................................................19
Appendix 6: Summary of model 2.........................................................................................................................20
Appendix 7: Code...................................................................................................................................................21
Table 1: Hierarchy Network...................................................................................................................................24
Table 2: Importance Network................................................................................................................................27

3. 3
Introduction
A network analysis was performed for the Global, Engagement and communication department within Jhpiego.
The purpose of the analysis was to find the interaction pattern within the department across all sub departments.
Being a non-profit, Jhpiego should ensure that it extracts maximum efficiency and no time is wasted on
miscommunications. Further an incentive program should be initiated that should encourage the informal network.
Data
A survey was sent to all the 40 employees within the GECO department and response was received from 33 of
them. The GECO department is further divided into 8 sub departments. Four networks were mapped. The first
network shows the 5 most important persons in a person’s network and asks them to rank based on the amount of
contact. The second network asks them to identify the hierarchical network of the persons they share information
with. The third network asks them to identify the frequency they share information and the fourth network asks
them to identify the valuable of the information they share. The persons were assigned the following attributes:
gender, age, tenure, department and role. The sample survey is given in appendix 1.
Analysis
For the analysis, two networks were picked: hierarchical and importance. Degree centrality, betweenness centrality
and clustering coefficient were mapped for each network. According to degree centrality, two different persons
were identified as central connectors for each network but for betweenness centrality and clustering coefficient, a
unique result was obtained for both the networks. For both the networks, there was a high correlation between
degree centrality and betweenness centrality. Following hypothesis were tested for further analysis: Refer Table
1&2 for all the values.
 Aged persons were more probable to give advice and hence they would be more important in the network
 Tenured persons were more probable to be important in a person’s network
 Persons within the same department were more probable to be important in a person’s network
The regression was run for degree centrality and age. No clear connection was established between the two
variables. (Refer Appendix 2). A network was mapped using R. The size of the node depicts the degree of the
person and the thickness of the edge represents the importance of the person.
To test the second hypothesis, a regression was run between Tenure and Degree Centrality. No clear connection
was established with low R squared, high p value and a very high range between the max and min residual. (Refer
appendix 3).
To test the third hypothesis, a regression was run between Department and degree centrality. No clear connection
could be established as Rsquared was very low and p value was pretty high. But by analyzing the network diagram,
homophile among the persons from the same department was visible. (Refer appendix 4)
Homphily was then checked in the importance network according to Age, Tenure and Department. The log
likelihood of linkage was likely to increase if the persons were in the same department. Low p value was also
observed. The log likelihood of linkage was also likely to depend upon the same age bracket of the person although
not as steep as that in the case of same department. (Refer appendix 5)
Homophily was again checked in the value of information network according to tenure and age. No clear
homophily could be established owing to high p values of the estimates. (refer appendix 6)
Conclusion

4. 4
The GECO department at Jhpiego has a strong vertical communication and weak lateral communication i.e it does
not communicate well across various sub departments of GECO. Moreover, the tenured persons are not seeked for
advice and are not important to anyone’s network. They should play an active role in communication owing to
their vast experience in the organization. A person not so significant in the hierarchy was identified to have high
degree centrality. Such important persons in the informal network shall be recognized and incentivized. There is
a lot of one way communication, so GECO needs to institute a change in which the communication is bi-
directional.

5. 5
What is y
Male
Female
Appendix 1: Survey
Social Network Analysis
Please help me with my class project by completing the attached survey. It will take 5 minutes or less of your
time. The survey is designed to map the communication network of your department and will result in both a
mathematical and visual representation of working relationships. The goal of the survey is to determine the role
of communication networks in organizational change.
What is your name?
our gender?
What is your age range?
20‐30 years
31‐40 years
41‐50 years
51‐60 years
>60 years
How long have you worked for Jhpiego?
Less than one year 1‐
3 years
4‐7 years
Greater than 7 years
In which area of the GECO department do you work?
MCSP Communications Legislation
Fundraising Events and Conference
Editing Management
Jhpiego Communications Graphic Design

6. 6
Which role correctly identifies you?
Vice President Web Designer/Specialist
Senior Manager Major Gifts Officer
Senior Administrator Advancement Manager
MCSP Communications team Lead Senior Development Coordinator
Director, Communication Graphic Designer
Publication and Design Director Administrative Coordinator
Legislative adviser and speechwriter Desktop Publishing Specialist
Events and Conference Manager Creative Service Manager
Communication Specialist/Manager/Coordinator Intern
Editor Others

7. 7
Please identify a total of five people w ho are important to you in your professional netw ork, w hom do you collaborate w ith for your w ork.
These people may be the ones w ho provide information to do your w ork, provide development support and advice in your day to day
w orking life. These people must come from the ones w orking in GECO. Please drag the options selected to the department they w ork
in.
Items
Melody McCoy
Michelle Boardman
Nicol Jenkins
Charlene Reynolds
Katrin DeCamp
Liz Eddy
Amanda Robbins
Ann LoLordo
Maryalice Yakutchik
Charles Wanga
Indrani Kashyap
Cole Bingham
Alisha Horowitz
Susi Wyss
Betsy Thompson
Sonia Elabd
Linda Benamor
Aimee Dickerson
Joel Bobeck
Alex Robinson
Young Kim
Latchia Anderson
Jamie Klemp
Renata Kepner
Gregory Davenport
Courtney Weber
Bekah Walsh
Dana Lewison
Deborah Stein
Sandra Crump
MCSP Communication Team Advancement
Editorial Services and
Communication
Publications and Design
Legislations
Events and Conferences Management (VP, Senior
Manager, Senior Administrator)

8. 8
Vipra Ghimre
Joan Taylor
Abby Becker
Kate Austin
Cynthia Morgan
Sara Haney
Jocabel Reyes
Yasmine Arsala
Anvit Goyal
For each person you identified, please rank them based on the amount of contact you have with them.
» Melody McCoy
» Michelle Boardman
» Nicol Jenkins
» Charlene Reynolds
» Katrin DeCamp
» Liz Eddy
» Amanda Robbins
» Ann LoLordo
» Maryalice Yakutchik
» Charles Wanga
» Indrani Kashyap
» Cole Bingham
» Alisha Horowitz
» Susi Wyss
» Betsy Thompson
» Sonia Elabd
» Linda Benamor
» Aimee Dickerson
» Joel Bobeck
» Alex Robinson
» Young Kim

9. 9
» Latchia Anderson
» Jamie Klemp
» Renata Kepner
» Gregory Davenport
» Courtney Weber
» Bekah Walsh
» Dana Lewison
» Deborah Stein
» Sandra Crump
» Vipra Ghimre
» Joan Taylor
» Abby Becker
» Kate Austin
» Cynthia Morgan
» Sara Haney
» Jocabel Reyes
» Yasmine Arsala
» Anvit Goyal

10. 10
For each person, you have identified, answer the following questions.
Hierarchal level
Frequency they provide you with
information that you use at work
Value of information they provide you
that helps you do your work
Higher Same Lower Occasionally Frequently
Very
Frequently
Occasionally
valuable
Valuable
Very
Valuable
» Melody
McCoy
» Michelle
Boardman
» Nicol
Jenkins
» Charlene
Reynolds
» Katrin
DeCamp
» Liz Eddy
» Amanda
Robbins

11. 11
Hierarchal level
Frequency they provide you with
information that you use at work
Value of information they provide
you that helps you do your work
» Ann
LoLordo
» Maryalice
Yakutchik
» Charles
Wanga
» Indrani
Kashyap
» Cole
Bingham
» Alisha
Horowitz
» Susi Wyss
» Betsy
Thompson
» Sonia Elabd
» Linda
Benamor
» Aimee
Dickerson
» Joel
Bobeck
» Alex
Robinson
» Young Kim
» Latchia
Anderson
» Jamie
Klemp
» Renata
Kepner
» Gregory
Davenport
» Courtney
Weber
» Bekah
Walsh
» Dana
Lewison
» Deborah
Stein
» Sandra
Crump
» Vipra
Ghimre
» Joan
Taylor
» Abby
Becker
» Kate Austin
Higher Same Lower Occasionally Frequently
Very
Frequently
Occasionally
valuable
Valuable
Very
Valuable

12. 12
Hierarchal level Frequency they provide you with
information that you use at work
Value of information they provide you
that helps you do your work
Higher Same Lower Occasionally Frequently
Very
Frequently
Occasionally
valuable
Valuable
Very
Valuable
» Cynthia
Morgan
» Sara Haney
» Jocabel
Reyes
» Yasmine
Arsala
» Anvit Goyal

13. 13
Appendix 2: Age vs Degree Centrality

14. 14
Call:
lm(formula = deg.imp ~ attri[, 3])
Residuals:
Min 1Q Median 3Q Max
-18.799 -8.351 -3.799 4.425 30.425
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 29.1264 5.3755 5.418 6 .47e-06 ***
attri[, 3] -0.7759 1.9300 - 0.402 0.69
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12.53 on 31 degrees of freedom
Multiple R-squared: 0.005186, Adjusted R-squared: -0.0269
F-statistic: 0.1616 on 1 and 31 DF, p-value: 0.6904

15. 15
Appendix 3: Tenure vs Degree Centrality

16. 16
Call:
lm(formula = deg.imp ~ attri[, 4])
Residuals:
Min 1Q Median 3Q Max
-20.041 -6.711 -2.372 3.959 27.289
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.032 5.742 3.488 0.00148 **
attri[, 4] 2.670 2.000 1.335 0.19169
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12.22 on 31 degrees of freedom
Multiple R-squared: 0.05434, Adjusted R-squared: 0.02384
F-statistic: 1.781 on 1 and 31 DF, p-value: 0.1917

17. 17
Appendix 4: Department vs Degree Centrality

18. 18
Call:
lm(formula = deg.imp ~ attri[, 5])
Residuals:
Min 1Q Median 3Q Max
-18.967 -7.052 -2.446 5.596 29.033
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.883 4.623 4.517 8.52e-05 ***
attri[, 5] 1.521 0.998 1.524 0.138
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 12.12 on 31 degrees of freedom
Multiple R-squared: 0.06971, Adjusted R-squared: 0.03971
F-statistic: 2.323 on 1 and 31 DF, p-value: 0.1376

19. 19
Appendix 5: Summary of model 1
Summary of model fit
==========================
Formula: imp2 ~ edges + nodematch("age") + nodematch("department") + nodematch("tenure")
Iterations: NA
Maximum Likelihood Results:
Estimate Std. Error MCMC % p-value
edges -2.4378 0.1446 0 <1e-04 ***
nodematch.age 0.4337 0.2115 0 0.0406 *
nodematch.department 1.6173 0.1974 0 <1e-04 ***
nodematch.tenure 0.3772 0.2064 0 0.0679 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
For this model, the pseudolikelihood is the same as the likelihood.
Null Deviance: 1463.9 on 1056 degrees of freedom
Residual Deviance: 784.5 on 1052 degrees of freedom
AIC: 792.5 BIC: 812.3 (Smaller is better.)

20. 20
Appendix 6: Summary of model 2
==========================
Summary of model fit
==========================
Formula: val2 ~ edges + nodematch("tenure") + nodematch("age")
Iterations: NA
Maximum Likelihood Results:
Estimate Std. Error MCMC % p-value
edges -1.9588 0.1170 0 <1e-04 ***
nodematch.tenure 0.3095 0.1992 0 0.121
nodematch.age 0.2383 0.2035 0 0.242
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
For this model, the pseudolikelihood is the same as the likelihood.
Null Deviance: 1463.9 on 1056 degrees of freedom
Residual Deviance: 848.5 on 1053 degrees of freedom
AIC: 854.5 BIC: 869.4 (Smaller is better.)

21. 21
Appendix 7: Code
library(igraph)
library(statnet)
setwd("/Users/anvitgoyal/Desktop/Courses/Year 2/Fall 1/Network Organizations/Project" )
# read data sets
importance <- as.matrix(read.table("importance.txt", sep=""))
heirarchy <- as.matrix(read.table("heirarchy.txt", sep=""))
freq <- as.matrix(read.table("frequency.txt", sep=""))
value <- as.matrix(read.table("value.txt", sep=""))
atr <- as.matrix(read.table("atr.txt", sep=""))
# attributes
attri<-as.data.frame(atr)
colnames(attri) <- c("id", "gender", "age", "tenure", "department", "role")
# create network objects from adjacency matrices and include also the attributes
imp <- graph.adjacency(importance, weighted = TRUE, mode = "directed") # importance network
heir <- graph.adjacency(heirarchy, weighted = TRUE, mode = "directed") # heirarchy network
fre <- graph.adjacency(freq, weighted = TRUE, mode = "directed") # frequency network
val <- graph.adjacency(value, weighted = TRUE, mode = "directed") # value network
##total degree
deg.imp<-degree(importance)
deg.heir<-degree(heirarchy)
deg.imp
## adjusting the size of the node according to its degree
V(imp)$size <- deg.imp/2
V(heir)$size <- deg.heir/1.5
##plot the network graphs
plot(imp, edge.arrow.size=.4, edge.width=E(imp)$weight, vertex.color="red")
plot(heir,edge.arrow.size=.4, edge.width=E(heir)$weight, vertex.color="blue")
##degree centrality
n<-length(V(imp))
deg.imp.centrality<-deg.imp/(n-1)
deg.imp.centrality
sort(deg.imp.centrality)
deg.heir.centrality<-deg.heir/(n-1)
deg.heir.centrality
sort(deg.heir.centrality)
## Export data into excel
install.packages("rJava")
install.packages("xlsxjars")
library("xlsx")
library(rjava)
library("xlsxjars")
write.xlsx(deg.imp.centrality, file = "degree.xlsx",append = FALSE)
write.xlsx(deg.heir.centrality, file = "degree.heir.xlsx",append = FALSE)
##betweenness centrality
bet.imp<-betweenness(importance)
bet.imp.centrality<- bet.imp/(n*(n-1)/2)
bet.heir<-betweenness(heirarchy)
bet.heir.centrality<- bet.heir/(n*(n-1)/2)
##Export data into excel

22. 22
write.xlsx(bet.imp.centrality, file = "bet.imp.xlsx",append = FALSE)
write.xlsx(bet.heir.centrality, file = "bet.heir.xlsx",append = FALSE)
#clustering coefficient for each person
clus.imp<-transitivity(imp,type = "local")
clus.imp
clus.heir<-transitivity(heir,type = "local")
clus.heir
##Export data into excel
write.xlsx(clus.imp, file = "clus.imp.xlsx",append = FALSE)
write.xlsx(clus.heir, file = "clus.heir.xlsx",append = FALSE)
#Correlations
cor.imp<-cor(indices.imp)
cor.heir<-cor(indices.heir)
##Export data into excel
write.xlsx(cor.imp, file = "cor.imp.xlsx",append = FALSE)
write.xlsx(cor.heir, file = "cor.heir.xlsx",append = FALSE)
#attributes plot according to age for importance
V(imp)$age<-attri$age
imp
par(mfrow=c(1,1))
vcolor<-rep("green",256)
vcolor[attri$age==2]<-"yellow"
vcolor[attri$age==3]<-"blue"
vcolor[attri$age==4]<-"orange"
vcolor[attri$age==5]<-"pink"
V(imp)$color<-vcolor
attrimp<-plot(imp, vertex.size=V(imp)$vertex_degree,
vertex.label.cex=0.7,edge.width=E(fre)$weight*2,edge.color="red",edge.arrow.size=0.2)
#legend("",legend=level(as.factor(V(imp)$age)),col=coul,bty = "n",pch = 20)
legend("topleft",
legend = c("20-30 years", "31-40 years","41-50 years","51-60 years","> 60 years"),
col = c("green","yellow","blue","orange","pink"),
pch = c(19),
bty = "n",
pt.cex = 1,
cex = 0.8,
text.col = "black",
horiz = F ,
inset = c(0.1, 0.1))
## Degree importance vs age regression
fit<-lm(deg.imp~attri[,3])
plot(fit)
summary(fit)
#attribute plot according to tenure for importance
V(imp)$tenure<-attri$tenure
imp
par(mfrow=c(1,1))
vcolor<-rep("green",256)
vcolor[attri$tenure==2]<-"yellow"
vcolor[attri$tenure==3]<-"blue"
vcolor[attri$tenure==4]<-"orange"
V(imp)$color<-vcolor
attrimp<-plot(imp, vertex.size=V(imp)$vertex_degree,
vertex.label.cex=0.7,edge.width=E(fre)$weight,edge.color="red",edge.arrow.size=0.2)
legend("topleft",
legend = c("<1 year", "1-3 years","4-7 years","> 7 years"),
col = c("green","yellow","blue","orange"),

23. 23
pch = c(19),
bty = "n",
pt.cex = 1,
cex = 0.8,
text.col = "black",
horiz = F ,
inset = c(0.1, 0.1))
## Degree importance vs tenure regression
fit1<-lm(deg.imp~attri[,4])
plot(fit1)
summary(fit1)
#attribute plot according to department for importance network
V(imp)$department<-attri$department
imp
par(mfrow=c(1,1))
vcolor<-rep("green",256)
vcolor[attri$department==2]<-"yellow"
vcolor[attri$department==3]<-"blue"
vcolor[attri$department==4]<-"orange"
vcolor[attri$department==5]<-"pink"
vcolor[attri$department==6]<-"grey"
vcolor[attri$department==7]<-"cyan"
vcolor[attri$department==8]<-"purple"
V(imp)$color<-vcolor
attrimp<-plot(imp, vertex.size=V(imp)$vertex_degree,
vertex.label.cex=0.7,edge.width=E(fre)$weight,edge.color="red",edge.arrow.size=0.2)
legend("topleft",
legend = c("MCSP communications", "Fundraising","Editing","JHpeigo
communications","Legislation","Events and Conferences","Mangaement","Graphic Design"),
col = c("green","yellow","blue","orange","pink","grey","cyan","purple"),
pch = c(19),
bty = "n",
pt.cex = 1,
cex = 0.8,
text.col = "black",
horiz = F ,
inset = c(0.1, 0.1))
## Degree importance vs department regression
fit2<-lm(deg.imp~attri[,5])
plot(fit2)
summary(fit2)
# create network objects from adjacency matrices and include also the attributes
imp2 <- network(importance, vertex.attr=attri, directed=TRUE) # advice network
heir2 <- network(heirarchy, vertex.attr=attri, directed=TRUE) # heirarchy network
fre2 <- network(freq, vertex.attr=attri, directed=TRUE)# frequency network
val2 <- network(value, vertex.attr=attri, directed=TRUE) # value network
#model: probability that importance of a person depends on age,department and tenure
f1 <- imp2~ edges + nodematch("age") + nodematch("department")+nodematch("tenure")
model1 <- ergm(f1, estimate="MPLE")
summary(model1)
#model: probability that value of information is dependent on tenure and age of person
f2<-val2~edges+nodematch("tenure")+nodematch("age")
model2<-ergm(f2,estimate = "MPLE")
summary(model2)

24. 24
Table 1: Hierarchy Network
Degree
Centrality
Betweenness
Centrality
Clustering
Coefficient
1 0.5 0.015625 0.466666667
2 0.625 0.072252558 0.222222222
3 1.25 0.218187762 0.168421053
4 0.5625 0.014614899 0.321428571
5 1.03125 0.300241867 0.104761905
6 0.53125 0.118856995 0.055555556
7 0.4375 0.115609217 0.142857143
8 0.8125 0.093652433 0.181818182
9 0.6875 0.077181925 0.266666667
10 0.53125 0.097626837 0.178571429
11 0.28125 0 1
12 0.6875 0.088005051 0.2
13 0.28125 0 0.833333333
14 0.4375 0.039525941 0.238095238
15 0.78125 0.195222312 0.177777778
16 0.3125 0.014864555 0.2
17 0.46875 0.049618343 0.428571429

25. 25
18 0.375 0.065527433 0.266666667
19 0.59375 0.02368859 0.361111111
20 0.4375 0.054410583 0.285714286
21 1.4375 0.205904418 0.169934641
22 0.46875 0 0.6
23 0.59375 0.146473255 0.083333333
24 0.625 0.030899908 0.222222222
25 0.34375 0.023029401 0.4
26 0.5625 0.149593951 0.138888889
27 0.40625 0.017058368 0.2
28 1.28125 0.243418971 0.189542484
29 1.21875 0.179732184 0.20952381
30 0.65625 0.12438447 0.277777778
31 0.40625 0.09625742 0.238095238
32 0.21875 0 0.7
33 0.46875 0.030050505 0.380952381

26. 26
Correlation
clus.heir deg.heir.centrality bet.heir.centrality
clus.heir 1 -0.476183304 -0.609582697
deg.heir.centrality -0.476183304 1 0.816674042
bet.heir.centrality -0.609582697 0.816674042 1

27. 27
Table 2: Importance Network
Degree
Centrality
Betweenness
Centrality
Clustering
Coefficient
1 0.5 0.015625 0.466666667
2 1 0.072252558 0.222222222
3 1.59375 0.219094778 0.168421053
4 0.71875 0.014614899 0.321428571
5 1.46875 0.326544226 0.104761905
6 0.8125 0.122616619 0.055555556
7 0.59375 0.098958333 0.133333333
8 1.25 0.101704545 0.181818182
9 1.09375 0.0777064 0.266666667
10 0.875 0.099331382 0.178571429
11 0.25 0 1
12 1.15625 0.086584596 0.2
13 0.375 0 0.833333333
14 0.6875 0.0390295 0.238095238
15 0.8125 0.196329539 0.177777778
16 0.625 0.013099747 0.3
17 0.6875 0.049239555 0.428571429
18 0.6875 0.072198714 0.266666667
19 0.90625 0.02368859 0.361111111
20 0.53125 0.035600321 0.333333333
21 1.75 0.233025387 0.175438596
22 0.625 0 0.6
23 0.75 0.156361473 0.083333333
24 0.9375 0.02979798 0.222222222
25 0.46875 0.023029401 0.4
26 0.75 0.134240239 0.166666667
27 0.4375 0.005208333 0.4
28 1.8125 0.242792955 0.196078431
29 1.1875 0.182378843 0.20952381
30 0.90625 0.122908168 0.277777778
31 0.65625 0.097527331 0.238095238
32 0.46875 0 0.7
33 0.625 0.03464695 0.380952381

28. 28
Correlation
clus.imp deg.imp.centrality bet.imp.centrality
clus.imp 1 -0.588629308 -0.636518088
deg.imp.centrality -0.588629308 1 0.802397961
bet.imp.centrality -0.636518088 0.802397961 1