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DATE DUE DATE DUE DATE DUE

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MSU Is An Afirmdlva Action/Equal Opponunity Institution
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NETWORK ANALYSIS AS AN INVESTIGATIVE TOOL
FOR ORGANIZATIONAL COMMUNICATION

BY

Thomas J. Larkin

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS

Department of Communication

1978

Accepted by the faculty of the Department
of Communication, College of Communication Arts,
Michigan State University, in partial fulfillment

of the requirements for the Master of Arts degree.

“xv -\

r
Director of Thesis

/

Guidance Committee: ,Chairman

 

 

 

 

3

specifies distanCes between points according to the reci-
rocal attern of relationshi s f n in t e dat .5 « -,» .
P P my} WWW (a w
ording to the Proctor and Loomis scheme A and B would be
located closest together when both A chooses B, and B chooses

A; A and B would be somewhat less close together if A chooses

( ..,, ‘ . r. \/
wit—324' In» " ‘

B, and B does not choosfifiejAK A and B would be even less close
if neither A or B choose each other; and, in turn, A and B
would be furthest apart if A rejects B, and B rejects A)

A similar attempt at standardizing the sociogram has
been made by Northway.6 The Northway technique results in
a "target sociogram" where those persons mentioned most
often, as contacts, are located in the center of several
concentric circles. As one moves away from this center,
individuals are placed on the appropriate circle according
to how frequently they are mentioned as contacts, with
Isolates (those with no contacts) located on the outermost
circle.

Standardizing the sociogram usually involves attempts
at formalizing the distances between points on the graph
according to some rule. However, in the standardization

techniques mentioned (Proctor and Loomis and Northway),

tWMWWfiw—fle
datmarierbiuwwmigéyf -
The techniques mentioned do not establish a metric space,
but instead several ordinal points (determined by the num-
ber of reciprocal relationship types or concentric circles)
and the intervals between these points are left to the

discretion of the investigator. In order for there to be

14.

a one to one correspondence between a given set of socio-
metric choices and a given sociogram (in the absence of
distances specified according to convention or fiat); it
would be necessary to transfer the lists of respondent
choices into a distance or spacial model. If one chooses

to do a spacial analysis of the sociometric choices, atten-
tion must be directed toward the dimensionality of the space,
finding and naming the principal dimensions, and determining
the configuration of points in the space.7 If however, one

chooses to do a network analysis of the sociometric_choige§,
attention must be dinested_12watd_anma_nrieri_seimcquxiter-
;a_uhich~whenmsatisfiedlconstitutewaqlingkwang_£he rimitive
units-inntheuanalysiswarehthose-peoplewwhomargflgonnggtggwbx
flamligxgmangmthgsempeople who.arelnntg, The problem being
considered -- the infinite number of sociograms which can
emerge from any single set of sociometric choices -- seems
to lead to at least two possible responses: 1) transform

the set of sociometric choices into a spacial configuration

(spacial analysis) or 2) treat each of the points, nr nes-

pandanxs._as_either.lia£ealerlae£_liake9 according to some

v "aw-fiCQM W

PrEVEBBEljaas飑.£sea~sryeaiallnetmnk.anaixgi§) -

Before proceeding with an examination of the two types
of analysis (spacial and network) several key theoretic dis-
tinctions need to be specified.8

The Meaning of awgero

In a metric space (a metric space being one which per-

 

mits a measurement of distance) a zero distance between two

points means that they are the same point. While in a

5

network analysis,(a zero merely implies the lack of a link
between the respective points and does not entail an iden-
tity.
The Symmetry of Measurement

In a metric space, the distance from A to B must equal
the distance from B to A. A network analysis. however does
not always assume that a link from A to B necessarily implies
a link from B to A. For example, the case where B can re—
ceive messages from A, but does not have the ability to
send messages in return.
The Rule of Triangular Inequality

In a metric space, some rule for triangular inequality
must be held such that the distance from A to B plus the
distance from B to C must be greater than or equal to the
distance from A to C. In addition, if the sociometric
choice list is to be represented in a Euclidean space, the
distances must conform to the more stringent rule that the
distance from A to C = (A2 + B2)l. Network analysis also
carries with it an assumption that if A is connected to B,
and B is connected to C; A is connected to C by a two-step
linkage. This assumption becomes of central importance when
the topic of matrix exponentiation as a tool for group struc-
ture investigation is discussed.
The Role of Motiqn

In a metric space, the motion that interests the inves-
tigators is that of the points located in the space. Motion,

in this metric space, should conform to some general rules

6
such as if a single point in the space is moved, the dis-
tance between that point and all other points in the space
should change; while the distance between any unmoved points
should remain constant.9 On the other hand, in a network
analysis, the investigator may be most interested not in
the movements of points or linkages, but in the movement of
a third variable along the linkage between two points. What
is dynamic in a network model is not the movement of points
or linkages (which would have no meaning in this nonspacial
analysis), but the movement of messages along the respective
linkages.

The discussion above is intended to explicate some of
the basic assumptions which may distinguish two types of
analysis performed on a sociometric choice list. It is now
necessary to look at the procedures involved in both the
network and spacial analysis.

In*a network analysis, the most primary item of inform-
ation_isflwheth§r or not_two individuals are linked. This
information may benparsimoniously stated in a matrix repre-
SEEEEEEEE_3£~£§E“g§ta' When“ ' ' , 'ce li 's
conxanied_inln_matrix form, themmgtrix i :

1) square; a matrix of order NxN, where N equals the
number of respondents,

2) binary; the elements of the matrix are made up of
zeros and ones, where zero signifies no link, and
one signifies a link,

3) conditional; the matrix N is conditional meaning
that the element in the ith row, jth column, n(i,j)
does not necessarily equal the element in the jth
row, ith column, n(j,i). If this condition were
true the matrix would be symmetric, n(i,j) = n(j,i).

7

One approach to exposing the subgroup formation within

10 A matrix

this matrix was developed by Forsyth and Katz.
was constructed so that each respondent had a number (1 to N)
which was listed across the top of the matrix (designating
columns) and along the side of the matrix (designating rows).
If, for example, respondent 16 reported a linkage with res-
pondent 2A, a one would be placed in the matrix cell located
in the 163g row, 24th column. By moving pairs of rows and
columns (the order of columns must always remain identical to
that of the rows) it is possible to get the ones in the mat-
rix to cluster around the diagonal. It can be easily shown,
for example, that if respondents 13, 14, 15, and 16, of
matrix N, all report linkages with each other, ones will tend
to cluster around the cells n(13,13), n (14,1u), n(15,15),
n(16,16) or along the diagonal. By moving people who report
similar linkages close to each other (in terms of rows and
columns) ones will cluster along the diagonal and subgroups
can be extracted. Weiss and Jacobson further identified the
structural components which can be specified once the clus-
ters are formed. Weiss and Jacobson identified a:11
1) Work Group (later to be called just a group) as
members who have linkages more with each other and
not with members of other groups.
2) Liaison, as an individual who had links with at
least two other individuals who were members of
groups other than his own; and,
3) Contact between groups (later referred to as a bridge)

as a single linkage between members of work groups
who would otherwise be classified as totally separate

groups.

8

One the rows and columns of the matrix have been suffi-
ciently manipulated that the "ones" (reports of contact)
cluster around the diagonal, the extraction of structural
components, subgroups, liaisons, and bridges may begin.
However, the manipulation of matrix rows and columns may be
an extremely time-consuming and difficult task, and as a
result, numerous algorithms have been developed to facilitate
the process. Two least squares techniques will be discussed
here, one developed by Katz and one by Beum and Brundage.

It should be remembered that any simultaneous reorder-
ing of rows and columns does not change the meaning of the
matrix, (only element positions) and thus the desired state
of the matrix (position of rows and columns) is one of maxi-
mized concentration of contacts around the diagonal. Katz
has developed a least squares equation which, when minimized,
designates this optimum ordering of rows and columns. Assum-
ing that the distance between any adjacent row or column is
one, the square of the distance of the element in the ith
row and jth column from the main diagonal is equal to
%(i-j)2.(:En order then to get the binary matrix into a form

where contacts are concentrated along the diagonal, it only

becomes necessary to minimizE) ei j (i-j)2, where ei j is
’ ’

the element (one or zero) in the ith row and jth column, and
12

the constant factor (é) is dropped. It can be easily seen
that the least squares equation will minimize as the (i-j)2
terms become smaller for each whole number entry. In turn,
the (i-j)2 terms will become smallest when the whole numbered

elements locate themselves around the diagonal. It should be

8

noted however, that while the least squares equation above

serves as an indicator of preferred form, it does not provide

much insight on the most efficient method for achieving this

form.

The technique developed by Beum and Brundage not only

results with contacts being clustered around the diagonal,

but contains, within its procedures, suggestions for the next

possible re-ordering of rows and columns to achieve this form.13

The rules for the Beum and Brundage technique are given

below:
1)
2)

3)

4)
5)

6)

column sums are obtained:

beginning with the bottom row, weights are assigned
to the rows of the matrix:

each column element is multiplied by its respective
weight and then summed:

the weighted sums are divided by column sums:

divided sums are ranked (one for the largest to N
for the smallest):

the column then with the highest rank (1) is moved
to the extreme left, and then corresponding row to
the top. -The next ranking column and row are then
placed next to the first and so on for the N rows
and columns.

An example matrix can be shown below:

Wts. A B C D E

5 A o 1 1 1 o

A B 1 O 1 1 1

3 C O O O O O

2 D O O 1 O O

1 E 1 O 1 O 0

col. sums 2 1 4 2 1
prod. sums 5 5 12 9 4
div. of sums 2.5 5 3 4.5 4
rank 5 1 4 2 3

Original Matrix

10

Revised Matrix
(rows and columns re-ordered)

B D E C A
B O 1 1 1 1
D O O O 1 O
E O O O 1 l
C O O O O O
A 1 1 O 1 O

The Beum and Brundage algorithm needs to be successive-
ly repeated on the matrix until 1) further iterations do not
cause a change in row or column position or 2) further itera-
tions result in an alternating pattern of row and column
orderings. When either of these conditions are met, the
squared distance of the contacts away from the diagonal will
be minimized.

Once the contacts become clustered around the diagonal,
it becomes necessary to locate the structural components.
This location of structural components can be accomplished
by visual inspection or computation according to some criter-
ia. Regardless of which technique is used, initial subgroup
formation is usually tentative and subject to further tests
of "groupness."

One common test of groupness in the sociometric litera-
ture involves the percent of ingroup communication. This
percentage is found by dividing the number of ingroup links
(links to other tentative group members) by the total number
of links for that respondent times 100. The investigator

may then require that each legitimate group member have at

least a certain percentage of his total communication with

11

other group members. Sociometricians have frequently set
this percentage criterion to 51.0% because 1) this figure
requires a substantial portion of one's communication to be
with other group members, and 2) this figure does not allow
any individual to be in more than one subgroup.

A second standard frequently used as a test of group—
ness is a maximum step linkage between members. It is possi-
ble to represent, in matrix formq<the minimum number of links
between any two group members. An entry of three, for example,
in the second row, fourth column, of the group linkage matrix,
would designate that group member number two was three links
away from group member number four, or in other words, a
message sent from group member two to group member four
would have to be transmitted through two other members.
Determination of these linkage distances by inspection of
a sociogram would be an extremely time consuming task: as an
alternative, Festinger has developed a matrix multiplication
procedure which significantly simplifies this task.

Festinger noticed that raising the binary matrix to
successive powers reveals the number of links between members,
that is, squaring the matrix reveals two step links, cubing

1b

the matrix reveals three step links, etc. If group member
A lists B as a contact, and B lists D as a contact, A has a
two step link connection with D. An example of a two-step

link exposed by matrix exponentiation is illustrated below.

12

Matrix of Contacts

A B C D E
A O 1 O O O
B O O O 1 O
C O O O O O
D O O O O O
E O O O O O

Squared Matrix of Contacts

A B C D E
A O O O 1 O
B O O O O O
C O O O O O
D O O O O O
E O O O O O

The one in the (A,D) cell of the squared matrix indi-
cates A and D are connected by a two-step link. It can be
easily shown that the entry in the squared matrix (a,d) or
(row 1, column4) cell is the sum of products of the elements
in the A row times the corresponding elements in the D col-
umn. The A row, in turn, can be interpreted as the people
A reports as contacts, and the D row as the people who re-
port contacts with D; as a result, when an entry in the A
row (people who A contacts) corresponds with an entry in the
D row(people who contact D) a two-step link is exposed.

The squared matrix is also capable of reporting the number
of two-step linkages between two members. For example, in
the matrix below, A and D are connected by two two-step

links, one through B and one through C.

13

Matrix of Contacts

A B C D

A O 1 1 O
B O O O l
C O O O 1
D O O O O
Squared Matrix of Contacts

A B C D

A O O O 2
B O O O O
C O O O O
D O O O 0

It was also noticed by Festinger, that the diagonal
elements in the squared matrix represented a two-step link
between a person and himself, or in network terminology, a
reciprocated contact (A reports a contact with B, and B re-
ports a contact with A). As a result, the squared matrix of
contacts is extremely rich in information as the following
interpretation will attempt to show.

Matrix of Contacts

A B C D
A O 1 O O
B 1 O 1 O
C O 1 O O
D 1 O O O

Squared Matrix of Contacts

A B C D
A 1 O 1 O
B O 2 O O
C 1 O 1 O
D 0 1 O O

14

Interpretation of Squared Matrix

1) A has one reciprocated link
A has one two-step link with C
2) B has two reciprocated links
3) C has one two-step link with A
C has one reciprocated link
4) D has one two-step link with B
D has no reciprocated links

Raising the matrix to a third power (postmultiplication
of the original matrix by the squared matrix) in turn, re-
veals the number of three-step links between any two members:
with the diagonal elements indicating the number of three-
step links between a person and himself, or in diagram form,
the number of triangles.

A B
C

This~diagonal element_in the cubed matrix can be extreme-
ly important because it does indicate this number of triangu-
lar group membership formations. Triangles, in turn, are
indicative of how highly structured the subgroup is; a
triangle (as opposed to a square or some other configuration)

isfla_gg£ji;§£§2_llnkagg_(ggmgly three) where all members of

the linkage also communicate directly with_ each other.L As a

-‘ u r. - “Humm-J

 

 

 

 

rgsul‘, in a triangular structure, the inter- -connectivity of

«wt—1 Amfl‘wm' —..._.-....._._

 

 

th__subgroup members is at a “maximumm. By adding together

"II-f!» v-II—w-v-

 

the diagonal elements of the cubed matrix of contacts for a
tentative subgroup, an inter-connectivity score for subgroup
members can be obtained. A possible test for a tentative

group structure might then be the sum of the cubed matrix

15
diagonal elements (number of triangles in the group) corrected
for the number of individuals in the group. A possible inter-
pretation for the cubed matrix of contacts could then be as
follows.

Matrix of Contacts

A B C D
A O 1 O O
B O O 1 1
C 1 l O O
D 1 O 1 O

Squared Matrix of Contacts

A B C D
A O O 1 1
B 2 1 1 O
C O 1 1 1
D 1 2 O O

Cubed Matrix of Contacts

A B c D
A 2 1 1 o
B 1 3 1 1
c 2 1 2 1
D o 1 2 2

Examples of Interpretation of Cubed Matrix

1) B has one three-step link with A
(B-D. D-C. C-A)

2) A is involved in two triangles

(A-B, B-C, C-A)

(A-B, B-D, D-A)
3) the total number of triangles for this subgroup is 9.
Luce and Perry explain that raising the matrix to addi-

tional powers (4th, 5th, 63h, etc.) will show respective

linkage distance between group members (number of 4—step

16

links, 5-step links, 6-step links, etc.).15 However, raising
the matrix past the third power introduces the problem of
repetitive linkage patterns. For example, a 6-step link
could actually be composed of A to B, B to C, C to D,AD to
B, B to C, C to C, and D to A, where several of the links
are actually being duplicated. The mathematical problem
here is also paralleled by a theoretical one which asks:
Of what meaning is it to have two group members who are six
links apart, or members who can only communicate with each
other via five other individuals? As a result, a common
criteria for subgroup formation is that no two group members
be greater than three links apart from each other.

Thus far, the analysis discussed as been based on link-
age or network assumptions where the primary variable is a
dichotomous one: are two individuals connected? It is now
possible to shift our analysis to a spacial paradigm, where
the primary variable is a continuous one involving distances.

Before looking at the sociometric choice matrix under
spacial assumptions, it will be necessary to transform the
matrix from a conditional state to a symmetric one (the
element in row i, column j, equals the element in row j,
column i). This revision is necessary so that the distance
from A to B equals the distance from B to A; and can be
accomplished by: 1) dropping unreciprocated links or 2)
forcing reciprocation. Either technique may be used as long
as the elements are mirrored along the diagonal; or a one in

row i, column j, corresponds with a one in row j, column i.

17

Once the matrix has been expressed in symmetrical form,
it is possible to think of each row as specifying the coordi-
nates of a point in N dimensional space, where N equals the
number of respondents.16 This matrix (or set of N row vec-
tors in N dimensional space) may be post-multiplied by its
transpose yielding a scalar product matrix where 2) the
diagonal elements equal the squared length of the respective
row vector (length of first row vector equals (1,1) ;
and 2) off-diagonal elements equal the product of vector
lengths times the cosine of the angle between them. In
turn, dividing the scalar product matrix by N (the number of
rows or columns) results in a variance-covariance matrix
where diagonal elements indicate the variance of reported
contacts for each respondent and the off-diagonal elements
indicate the covariance of reported contacts for any two
respondents.

By working with standardized score, (dividing the devia-
tions from the mean of each column, by the standard deviation
for the same column), the variance-covariance matrix reveals
correlation coefficients with unity on the diagonal elements
and correlations between respondent choices on the off-dia-
gonal elements. From this correlation matrix, it becomes
possible to factor analyze the choice patterns among respon-

dents under the assumption that individuals will cluster

together in the space, when they make similar sets of choices.

When the matrix is factor analyzed, each factor should repre—
sent a whole subgroup, with the dimensionality of the space

determined by the number of subgroups. And in turn, an

17

18
individual's membership among the subgroups can be inter-
preted through his set of respective factor loadings.

In review, it can be seen that the original sociometric
choice list left too much variance as to the number and type
of sociograms which could be constructed from a single data
set. As a result, attention was turned toward representing
the choice list in matrix form, and decomposing this matrix
into subgroups using assumptions of a linkage (network) ana-

lysis or a spacial (distance) analysis.

PROCEDURES AND METHODS

OF NETWORK INVESTIGATION

In this section, attention will be given to the sample,
testing procedures, questionaire, and data analysis method
used in gathering and analyzing the data.

\.

Sample 9%

The sample used in this investigation was the Lansing
Junior League of Women, of Lansing, Michigan. Membership
in this organization is divided into three sections: 1)
provisionals(ffirst-year tentative membership in the league;
2) actives, normal functioning members: and 3) sustainers,
members who only pay dues to maintain formal membership.

The following characteristics are descriptive of the League
membership:
1) all participants live in the mid-Michigan area:
2) ninety-eight percent of the members are married:
3) ninety percent of the members have children;

4) thirty percent indicate part-time or full-time
jobs;

5) total league membership is 393 women composed
of: 22 provisionals, 144 actives, 217 sustain-

ers, and 11 of no known status. /’ 31A
'12“ Li
Procedure ./;3

The network analysis being reported here was part of an

larger’and‘more—comprehensive‘investigation of totai~£eague
operations.18 Between January ‘and_May‘6f‘T9?5——feurflquest-

iongizes—were-distributsd'ffi'thé“League assessigg the corres-

pondence between multi-dimensional attitude configurations

 

 

and reports of overt behavior. On May 20, 1975, the network

19

NFL/1

\

t 20
questionaire was mailed to 22 provisionals, 144 actives,
and 65 sustainers. After one week, actives and provisionals

who had not returned their questionaire were called by tele-

O\‘\(J/‘ : )

phone and asked to do so. After four weeks, the return rate

was as follows:
L'\ R

1)222% return of "actives" questionaires
2) 80% return of "sustainers" questionaires
3)091% return of unknown status

4);9£% return of provisionals .3 z ‘

"

It should be noticed, however, that oniyeéé of the 2G?

sustainers (30%) were actually sent questionaires. Given

)
4C.

the limited role which thse sustainers play in the League,

it was not felt that obtaining data from the entire population

‘

of sustainers was worth the=ex§ense. As a result, the 65
questionaires sent to sustainers were selected from a ran-
dom number table, and the 52 questionaires received represent
80% of the questionaires sent, but only 24% of the total
number of sustainers.

Questionaire

The design for the questionaire was primarily adopted

frnmzanacobson/afid\seash6?e\questionaire/devgloped for an

early organizational network study.19 r \

" T1)

The cover page of the questionaire informed each respon-
<1”~‘[3i( ‘)

dent, that the communication research team was performing an

  

"Information Flow Study" of their organization. Each res-
pondent was then asked to 1) place their name at the top of
the questionaire, 2) complete the questionaire, and 3) return

the questionaire to the Department of Communication, Michigan

\N

22
Two comments about questionaire design are in order.

The first is that the respondent categories under the

V'*"\

"Subject Matter" scale werefgiiensmore precise definitions

at Wtfi'é’p‘ééé‘fasfoiiows:

Personal Issues: "Conversations where your own
personal feel1ngs about League activities are
discussed."

Social Issues: "Conversations where others' ex-
_pectations, family friends, neighbors, about
your League activities are discussed."

Situational Issues: "Conversations where the
requirements of League activities are discussed
(e.g., difficulty of activity, time spent work-
ing, effort, responsibilityifgtc.)"

\pfi ‘ 3 L“

The second comment is that(thgmgichotomouswchoice_used
to designate initiator of contact proved unsuccessful. Res-
pondents consistently indicated that over the range of con-
tacts with another individual initiation could only be
reported as a proportion or percent and not as a yes or no.
As_a result, this question was dropped from the data anal-
91.8.18-

Data Analysis

The primary method of data_analysis_g§ggmin this study

Iva-gnu“ V- a. “-

 

is_a network analysis program_written by William D. Richards

""d' 4"

 

Jr., and stored in a CDC 6500 computer at Michigan State

 

University.20 In_abbreviated fprmifltheflnetwork,analysis

algorithm is one.which lists the respondentsmlwtdwN along

a continuumywand then computes a mean_contactee,score for
W" 7

each respondent. “The mean-contactee score is derived from

.45- our-w“.._...

thg_§EE12i1Bllflcontactee«numbers.dividedmby_the total number

V "‘ ‘v—n—v q- o-w~v.—'qp rp-q...‘

of contactees. The respondents are then re-ordered along the
tn._._p-qr-——""’-—'"' "W “I”- ‘ I I ' " "' ' ~.. -- . . -_- ... ....__.

23

continuum according to their mean contactee score. When
Wm -..

this iterative procedure~is performed a number of times,
_the resultant continuum contains clusters of respondents
who have made similar contact choices. Then, inaamsomgwhgt
metaphorical sense, a scanning radius measures the distance
between consecutive*respongentswtqmdetermine,whethgr the

#—

clusters are close enough to eaghflqther_tgwggnstitutemgwsub-

M Iw.‘ m..-

group., In a more precise sense,«the scanning radius (Whose
diameter may be determined by the investigator) centers on
each_respondentwandflrecordswtheenumber ofuother1respondents
to the left and right of the centered respondent which still
fall within the radius. Once this haswbeen accomplished for
each respondent, it is possible to establish a ratio of non-
overlapping to overlapping structures. Por example, the
scanning radius centered on respondent SOIreveals 3 respond-
ents to the left and 2 respondents to the right; while when
centered on respondent ZE’revealsh3‘respongentsmtgwtheflleft
and 5 respondents to the right, the non-overlapping to
overlapping ratio does not experience much change, while

group boundaries will be indicated by relatively large shifts

in the ratios between.respondents. Thandifferéfibe’ifi‘ratios'

(fr-r“

neededmto/ferm~a~subgrcupJermalbcundafy‘banfbe~eentrcIIed
byxthexinwestigat3?7—’/i

It should be noted that the procedure discussed above is
used only in the formation of tentaive group structure,
and that further requirements (e.g., 51% ingroup communica-

tion) are usually specified by the examiner.

FINDINGS

This section will analyze the data at two hierarchic
levels of abstraction: 1) the structure of the network as
a whole, and 2) the decomposition of this network into
structural components.

.23 is assumed.hg;: that the network as a whole should
exhibit some kind of structure, such that some individuals
have a large chance of being linked, while for others, this
chance is somewhat smaller. In other words, the assumption
of a structured network is an assumption of deviance between
the network structure revealed in the data, and the network
structure expected from a totally random network. For the
purposes of this analysis, a highly structured communication
network is one which contains high variance of linkages
between members, or where differential position in the org-
anization requires differential use and number of communica-
tion linkages. 0n the other hand, a random communication
network makes the assumption that any two organizational
members have an equal chance of a communication linkage.
Looking at the deviation in the variances of these net-
works is in many ways a test of our obtained network under
the assumption of a structured communication organization.

Before proceeding, it is necessary tq/gefine what is
meant by a link. A link is normally indicated when a res-
pondent reports a communication contact with another
organization member: a reciprocated link is’where the con-

Z~

tactee also reports'this link. f the 494?links reported
3

by respondents, Efii or 20% were reciprocated (A reports B,

23

24
and B reports A). Two options are left open to the investi-

gator, 1) to drop 393

 

eciprocatedfllinks'gr 2) add 393
links to force reciprocat nf” Different procedures are
listed and usgdwamfdifferen times in this analysis and will
be designated beforehand.

In order to ascertain whether a significant difference
exists between the obtained network structure and a random
network, an F test of linkage variance needs to be performed.

The variance of forced reciprocated links in the obtained

network can be derived from the following equation.

 

n
2 i=1 (1. - '1')2
s = 1
o
N
where,
SE = variance of obtained network
1.1 = number of links per respondent
I = mean number of links across all respondents
N = number of respondents

The mean number of links was, in turn, found by dividing
the total number of links (the links reported plus the links
added for reciprocation) and dividing by N or 394 respondents
Substituting values in the variance equation yields:

2 _
SO "" 273014'6

According to the binomial expansion, the variance in

the number of links for the expected random network can be

expressed as:21

25

n p q, where:

 

 

n = the number of chances for a link for each
respondent or (n-l)
p = the probability of any given pair of res-
pondents being linked or L (total number of
N (N-l) links)
q = the probability of any two respondents not
being linked or 1-p or:
N (N-l) - L
N (N-l)
Therefore, the equation looks as follows:
N-l - -
npq = ( ) . L . N (N 1) L
N(N-1) N (N-l)
or,
npq = 2.20
and,
2 _
Sexp — 2.20

An F test with degrees of freedom 393 and 393 shows a
significant difference between the networks at .001 signifi-
cance level, and thus supports the assumption that the net-
work revealed in the data significantly differs from what
would be expected of a randomly structured network.

A further test of significance needs to be applied to
this data, however, due to the particular nature of this
organization. Within the League are a large number of sus-
tainers, who perform few functions in the League, and thus
are involved in little or no League communicative acts.
Inclusion of these sustainers into the previous analysis
greatly inflated the squared deviations from the mean and

resultantly, the variance. It should be advisable to compute

26
the F-test again, excluding these marginal members from
the analysis. The F ratio of variances obtained in this
manner is somewhat smaller than the initial one, but still
shows a significant difference between the obtained network
and random networks at the .001 significance level. It can
thus be determined that the distribution of links found in
the data significantly differs from that which would be
expected in a random model.

The preceding discussion was directed at the wholistic
properties of the network: this portion on the other hand,
focuses on the structural components which may be detected
by the network program. These structural components include:

1) Group Members: Individuals whose communication

links are more with other group members than non-
members.

2) Bridge: A person who is a member of a communica-

tion group and has a link to a person who is a

member of a different group.

3) Isolate: An individual in the network who has
fewer than two communication links.

4) Liaison: A person within a network who has links
with two or more communication groups, but does not
have a majority of links with any one group.

The most fundamental component in this network analysis

 

,/ is the link, or that which indicates the communication
relationship between people. The study being reported here
used two variables (weights) to characterize each communica-
tion link. Respondents were asked not only to identify the
other participant in their communicative interaction (the
link), but to characterize this relationship according to

its frequency and importance. These frequency and importance

27
ratings were then used to assess the strength of each link
according to the equation:
Strength of a link = (X + Y) + (X ' Y)
where, .

the strength of the link from one
person to another,

Strength
X = the frequency rating given to the link

(1 to 5, where 5 is greatest frequency)

Y = the importance rating given to the link

(1 to 5, where 5 is greatest importance)

This link weighting procedure serves two special functions
in the decomposition of the entire network into structural
components. First, by directing the program to only look
at links of some minimum strength, it is possible to elimi-
nate those links from the analysis which are relatively
infrequent and lacking in importance. Second, the group
percentage criterion (what percent of one's communication
must be with other group members in order to be in the group)
looks at the percent of strengths and not the number of links
per se.

Before revealing the structural components of this net-
work, a cautionary comment is in order. The network program
used in this study offers the investigator considerable
flexibility in the determination of program parameters, and
thus similar influence in the decomposition routines of the
program. Changes in the following parameters, for example,
result in considerably different determinations of group

membership, isolates liaisons, etc.

28

whether unreciprocated links are
dropped, or links added to force

Parameter 3

reciprocation,
Parameter 10 - the minimum strength which a link
- must have to be included in the analysis
Parameter 14 - the width of the scanning radius,
Parameter 15 - the maximum path length (number of

links) which may separate any two
group members,

Parameter 36 - percentage criterion for group
membership.

The point to be made here is that an experienced user of
this program can so specify the parameters to control the

decomposition of the network. Whether the network breaks

_..---

down into a few groups_ with high,connectivity amongst its

\ gal—0"..- ‘ ‘ annuals-h.—

members, or many groups with few inter-group links can fre-

quently be directed or controlled by the experimenter. As

manna-urn...

 

 

a result, it seems advisable to specify the parameters in-
volving network decomposition into structural components
prior to actually running the data.

The initial value of the parameters used, and the struc-
tural components found in this network are recorded in
Table I. With the parameter values so specified (using
forced reciprocated links) the program could find only one
large group (N=112) in this network. Three reasons suggest
that this might be an accurate representation of the com-
munication structure in this organization. First, the

organization is a volunteer one, and an attempt to force a

--_flw

 

 

v. a": n—w” q.—
-m
w—

strict hierarchical communication structure (such as an

r: r.» —
—_..._._ _ w..—
‘h— '- Ir --- "- H " ‘-

organizational chart) might meet with resistance or desertion.

Second, the communication structure of the organ1zat1on

\\ --.—

m--

 

29
seems to be not that of a multi-leveled organizational

chart, but of a circle with several activgfl(ignthe communir

k

cative¥sense) individuals,in,the.center and numerous isolates

"d‘

 

“my. - ‘-

around the fringe. Third, an inspection of the deviation

scores used in computing the variance of links in the ob-

tained network revealed two groups,(§hose Who had many links

 

 

(and therefore high deviation scores) and those that had

- - fl, .‘FWC-n—H [M
w,”

 

one or no links (and therefore high deviationnssorgs). As
would be expected, an inspection of the subgroup with high
deviation scores due to many links, tended to have these
links between each other. In conclusion, the analysis dis-
cussed here seems to suggest that the organization can be
characterized-as hayingwgne centralflgrqu (29% of the mem-
bers) whichensases ina-larsesamount stingergfilikiom'
municationrmandma large number.of.individualsamba—haxeafewer
thmmm.

The question may now be rephrased however to ask, what
group or linkage criterion are necessary to break up this
large central group? This question calls for an after-the-
fact alteration of program parameters to facilitate the de-
composition of this network.

The parameters values used for the structural components
found are recorded in Table II. In this case, the network
was decomposed into three groups (N=35, N=3, N=56). The pri-

mary changes in parameters which may account for this struc-

turing are:
Parameter 11 — minimum weight for a link
Parameter 14 - width of scanning radius

Parameter 36 - group percentage communication
criterion

30

The primary effect of these parameter changes was to
1) drop linkages from the analysis which were relatively
infrequent or unimportant (this took the greatest proportion
of links away from the "active" communicators, for while
these isolates had few links they tended to use them fre-
quently and see them as having high importance); 2) to
decrease the potential size of group boundaries by decreasing
the scanning radius and 3) to generally make it easier to
be in a group (with a percentage criterion of 40% it was
even possible to be in two subgroups. This, however, did
not occur.) If the program is instructed to look only at
high frequency, high importance links with decreased poten-
tial group boundaries and eased percent of necessary in-
group communication, three groups can be found in the
network.

In summary, this section has attempted to look at the

 

-*_.._-.

network in_wthistic terms, as a contrasted unity with a

_.
--

 

*—
"'-*-I--——- -—.._ ‘- I, --q—.—.— u. _.- —-.--v-

random networkt‘and in strugtural_terms asnthe different_

components which make up the network.

10.

11.

FOOTNOTES

For a discussion of the various definitions of socio-
metry see: Bjerstedt, A. (1956) Interpretations of
Sociometric Choice Status. Copenhagen: Muskgaard.

Network analysis has been done on some variables not
directly related to communication. For a more thorough
discussion see: Wigand, R. T., and Larkin, T. J.,
"Interorganizational Communication, Information Flow and
Service Delivery Among Social Service Organizations:"

a paper presented to the International Communication
Association, 1975 Convention.

Moreno, J. L. (1934). Who Shall Survive? Washington,
D.C.: Nervous and Mental Disease Monograph, No. 58.

Borgatta, E. F., (1951). A Diagnostic Note on the Con-
struction of Sociograms and Action Diagrams. Groups, p.
3, 300-308.

Proctor, C. H. and Loomis, (1951) Analysis of Sociometric
Data. In Marie Jahoda, M. Deutsch, and S. W. Cook (Eds)

Research Methods in Social Relations: With S ecial Re-
ference to Prejudice. Part 2, New York: Dryden. p. 561-
585.

Northway, Mary L. (1940) A Method for Depicting Social
Relationships Obtained by Sociometric Testing. Socio-

metry, 3, p. 144-150.

 

For a detailed discussion of spacial and linkage analysis
see, Roistacher, Richard 0., " A Review of Mathematical
Models in Sociometry" Sociological Methods and Research,
Vol. 3, No. 2, November 1974.

Roistacher, Ibid., pg. 151.

For a more complete discussion of the assumptions in-
volved in spacial and network models see: Craig, Robert
T. "Models of Cognition, Models of Messages and Theories
of Communication Effects: Spacial and Network Paradigms."
Paper presented at the International Communication Asso-
ciation, Chicago, Illinois, 1975.

Forsyth, Elaine, and L. Katz (1956). A Matrix Approach
to the Analysis of Sociometric Data: Preliminary Report.

Sociometry, 9, 340-347.

Weiss, Robert S. and Jacobson, Eugene, A Method for the
Analysis of the Structure of Complex Organizations.

American Sociological Review, 1955, Vol. 20, 661-668.

31

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

32

Katz, Leo, On Matrix Analysis of Sociometric Data,
Sociometry, 1947, 10, 233-244.

Beum, C. 0., and E. G. Brundage, A Method for Analyzing
the Sociomatrix, Sociometry, 1950, 13, 141-145.

Festinger, L., The Analysis of Sociograms Using Matrix
Algebra. Human Relation, 2, 1949, 153-158.

Luce, D. R., and A. D. Perry, A Method of Matrix Analysis
for Group Structure, Psychometrika, 1949, 14, 95-116.

Van de Geer, John P., Introduction to Multivariate Anal-
ysis for the Social Sciences W. H. Freeman and Co.,
San Francisco, 1971) p. 18.

An example of factor analysis used on a sociometric
choice matrix is: Bock, R. D., and S. Z. Husain, An
Adaption of Holzingers B-Coefficients for the Analysis
of Sociometric Data. Sociometry (1950) 13, 146-153.

Seibold, David R., A Complex Model of Multidimensional
Attitude and Overt Behavior Relationships: The Mediat-
ing Effects of Certainty and Locus of Control. Ph.D.
Thesis at Michigan State University, 1975.

Jacobson, E., and Seashore, 8., Communication Practice
in Complex Organizations, Jggrnal of Social Issues, 1951,
VOlO 7, #3, 28-40.

For more information about the technique see: Richards,
William D. Jr., Network Analysis in Large Complex
Systems: Technique and Methods-Tools. Paper presented
to 1974 International Communication Association, April
16-21, 1974.

Richards, William D., Jr., Network Analysis in Large
Complex System: Metrics. Paper presented to 1974
International Communication Association, April 16-21,

1974.

Monge, P. and Lindsay, G. N., The Study of Communication
Networks and Communication Structure in Large Organiza-
tions. Unpublished paper at Michigan State University,
Department of Communication.

TABLE I
VALUES

GROUP MEMBERSHIP AT INITIAL PARAMETER

Network Analysis Porgram Version 4.0 Sept. 1974
Copyright 1974. Nilliam O. Richards Jr.

CONTROL PARAMETERS

PARAMETER N0. 1 (N 0F NODEs) VALUE: 349 **USER**
PARAMETER N0. 2 (N OF LINKS) VALUE: 700 *“USER**
PARAMETER N0. 3 (RECIPROCAT) VALUE: 1 **USER**
PARAMETER NO. 4 (DIRECTION) VALUE: 0 **USER**
PARAMETER N0. 5 (N OF ITERS) VALUE= 4 **USER**
PARAMETER N0. 6 (N RAN PRNT) VALUE: 3 **USER**
PARAMETER N0. 7 (DATA UNIT ) VALUE: 60 **USER**
PARAMETER N0. 8 (OBSv/CARD ) VALUB= 7 **USER**
PARAMETER N0. 9 (NAME-NIDTH) VALUE= 9 **USER**
PARAMETER N0. 10 (LON HEIGHT) VALUE: 1 **USER**
PARAMETER N0. 11 (HI MEIGHT ) VALUE: 35 **USSR**
PARAMETER N0. 12 (EXPONENT ) VALUE: 1 **USER**
PARAMETER NO. 13 (DNSTY HIST) VALUE: 1 **USER**
PARAMETER N0. 14 (SCAN RDIUS) VALUE: 200 **USER**
PARAMETER N0. 15 (MAX PATH L) VALUE= 10 **USER**
PARAMETER N0. 16 (LOT S. N0.) VALUE: 1 **USER**
PARAMETER N0. 17 (FILE OJTPT) VALUE: 0 **USER**
PARAMETER NO. 18 (PRINTO SUP) VALUE: 0 **USER**
PARAMETER NO. 19 (GRID SUP ) VALUE= 0 **USER**
PARAMETER N0. 20 (GROUP SUP ) VAL°E= 0 **USER**
PARAMETER NO. 21 (MAX OUTPUT) VALUE= 15 **USER**
PARAMETER N0. 22 (MIN SPLIT ) VALUE: 12 **USER**
PARAMETER N0. 23 (GRP-SNSVTY) VALUE: 100 **USER**
PARAMETER N0. 24 (SPLITDEv ) VALUE= 30 **USER**
PARAMETER N0. 25 (UNUSED ) VALUE: 0 DEFAULT

PARAMETER N0. 26 (UNUSED ) VALUE: 0 DEFAULT

PARAMETER N0. 27 (UNUSED ) VALUE: 0 DEFAULT

PARAMETER N0. 28 (UNUSED ) VALUE: 0 DEFAULT

PARAMETER N0. 29 (UNUSED ) VALUE: 0 DEFAULT

PARAMETER N0. 30 (UNUSED. ) VALU3= 0 DEFAULT

PARAMETER NO. 31 (UNUSED. ) VALU“= 0 DEFAULT

PARAMETER NO. 32 (UNUSED ) VALUE: 0 DEFAULT

PARAMETER N0. 33 (DETAILS ) VALU“= 0 DEFAULT

PARAMETER N0. 34 (MEAN STRST) VALUE= 0 DEFAULT

PARAMETER N0. 35 (PUNCH DECK) VALUE: 0 DEFAULT

PARAMETER N0. 36 (FERN ) VALUE: 51.000 **USER**
PARAMETER NO. 37 (CONS ) VALUE= .000 **USER**
PARAMETER N0. 38 (MR ) VALUJ= 1.000 **USER**
PARAMETER NO. 39 (MY ) VALUE: 1.000 **USER**
PARAMETER N0. 40 (CCX ) VALUE: .000 **USER**
PARAMETER N0. 41 (CCY ) VALUE: .000 **USER**
PARAMETER NO. 42 (MCPx ) VALUE: 1.000 **USER**
PARAMETER N0. 43 (DROP-SPLIT) VALUE: .100 **USER**
PARAMETER N0. 44 (2-STEP NI ) VALUE: 1.000 DEFAULT

PARAMETER N0. 45 (UNUSED ) VALUE: .000 DEFAULT

33

100
102
104
105
106
107
108
109
112
113
114
117
124
125
126
127
128
130
131
132
135
136
137
138
139
140
141
142
143
145
146
147
158
151
152
153
170
174
187
197
243
266

34

GP. 0UP NUNZEER 1

HI—‘l—‘HHHHHHH
\OCDVOM-PUNHOOQVO\\RPWNH

NNNNNNNNNN
\OC(3\)O\U\-F'\AJNHO

WWW
NHO

HAS 1 l 2

-_'—
i

. (I‘c:*:q‘1
Lapping; D

109.
110.
111.
112.

282
289
292
326

35

54.

55-

CD 0’)
(I‘m

TABLE II
GROUP MEMBERSHIP AT REVISED PARAMETE; VALUES
Network Analysis Program Version 4.0 Sept. '74
Copyright 1974. William D. Richards, Jr.
CONTROL PARAMETERS

PARAMETER N0. 1 (N 0F NODES) VALUE: 394 **USER**
PARAMETER N0. 2 (N 0F LINKS) VALUE- 900 **USER**
PARAMETER N0. 3 (RECIPROCAT) VALUE: 1 **USER**
PARAMETER N0. 4 (DIRECTION ) VALUE: 0 **USER**
PARAMETER N0. 5 (N 0F ITERS) VALUE: 4 **USER**
PARAMETER NO. 6 (N RAN PRNT) VALUE: 15 **USER**
PARAMETER N0. 7 (DATA UNIT ) VALUE= 60 **USER**
PARAMETER N0. 8 (OBSV/CARD ) VALUE: 7 **USER**
PARAMETER N0. 9 (NAME-NIDTH) VALUE: 0 **USER**
PARAMETER N0. 10 (LON NEIGHT) VALUE: 8 **USER**
PARAMETER N0. 11 (HI NEIGHT ) VALUE= 35 **USER**
PARAMETER NO. 12 (EXPONENT ) VALUE: 1 **USER**
PARAMETER NO. 13 (DNSTY HIST) VALUE: 1 **USER**
PARAMETER NO. 14 (SCAN RDIUS) VALUE: 150 **USER**
PARAMETER N0. 15 (MAX PATH L) VALUE= 3 **USER**
PARAMETER N0. 16 (LON S. N0.) VALUE: 1 **USER**
PARAMETER N0. 17 (FILE 0UPT ) VALUE: 0 **USER** ,
PARAMETER N0. 18 (PRINTO SUP) VALUE: 1 **USER**
PARAMETER NO. 19 (GRID SUP ) VALUE: 0 **USER**
PARAMETER N0. 20 (GROUP SUP ) VALU“= 0 **USER**
PARAMETER N0. 21 (MAX OUTPUT) VALUE: 15 **USER**
PARAMETER N0. 22 (MIN SPLIT) VALUE: 12 **USER**
PARAMETER N0. 23 (GRP-SNSMTT) VALUE: 120 **USER**
PARAME ER N0. 24 (SPLITDEV ) VALUE: 30 **USER**
PARAMETER N0. 25 (UNUSED ) VALUE: 0 DEFAULT
PARAMETER N0. 26 (UNUSED ) VALUE: 0 DEFAULT
PARAMETER N0. 27 (UNUSED ) VALUE: 0 DEFAULT
PARAMETER N0. 28 (UNUSED ) VALUE: 0 DEFAULT
PARAMETER N0. 29 (UNUSED ) VALUE: 0 DEFAULT
PARAMETER N0. 30 (UNUSED ) VALUE: 0 DEFAULT
PARAMETER N0. 31 (UNUSE ) VALUE: 0 DEFAULT
PARAMETER NO. 32 (UNUSED ) VALU“= 0 DEFAULT
PARAMETER N0. 33 (DETAILS ) VALUE= 0 DEFAULT
PARAMETER N0. 34 (MEAN STRST) VALUE: 0 DEFAULT
PARAMETER N0. 35 (PUNCH DECK) VALUE: 0 DEFAULT
PARAMETER N0. 36 (FERN ) VALUE: 45.000 **USER**
PARAMETER N0. 37 (CONS ) VALUE: .000 **USER**
PARAMETER N0. 38 (MX ) VALUE= 1.000 **USER**
PARAMETER NO. 39 (MY ) VALUE: 1.000 **USER**
PARAMETER N0. 40 (CCX ) VALUE: .000 **USER**
PARAMETER N0. 41 (CCY ) VALUE: .000 **USER**
PARAMETER NO. 42 (MCPK ) VALUE= 1.000 **USER**
PARAMETER N0. 43 (DROP-SPLIT) VALUE: .100 **USER**
PARAMETER N0. 44 (2-STEP NT ) VALU“= 1.000 DEFAULT
PARAMETER NO. 45 (UNUSED ) VALUE: .000 DEFAULT

36

GROUP

HH
HO\OCI)'\)O\UI-F'\.~JNH

12.

NNNHHHHHHH
NHOOmVO\UI-P’w

NNNNNNN
\O(I)\}O\UI-P\A)

muuuuw
Kn PM.) N HO

NUMBER

111A.“

U

GROUP NUI’JBER 2 HAS

1.
2.
3.

GROUP- i‘IUI‘ABER 3 HA

VQMPUNH

31
130

357

3 MEMBERS

56 MEMBERS

61
64

97

112
113
114
124
125
126

' 127

135
136
137
138
139
141
142
146
150
152
153
170
187
243
282
289
292
326

-4—

4) The average importance of the communication.

Answering these questions will allow us to discover the networks
or routes which interpersonal messages take as they flow through
the League’s organizational structure.

**********

Do you
Please write in the names of FREQUENCY OF CONTACT usually
those people in the League initiate

with whom you have most con- -3 «, >6" j?__ a this contact?
tact and answer the questions 3., ,. f} *3; 2::- 33 >~

to the right. 3,;‘3 '3 °,§: 5,20 33:3

Names of board members ‘1? _Q_ 11‘} V3; ‘11‘_ 1‘72

or other officers 4 5 1

gamglc -. 2’0: _ I/., .__ _ _ .Z

 

U

 

 

 

 

lllllllfi

 

Names of other actives whom
you contact.

 

 

 

 

 

 

Names of other provisionals,
transfers or sustainers whom
you contact.

 

 

 

 

 

- o -

 

*Conversations where your own personal feelings about league activities are
discussed (e.g., enjoyment, satisfaction, disappointment, etc.)

**Conversations where others' expectations, family, friend, neighbors, about your
league activities are discussed.

***Conversations where the requirements of league activities are discussed (e.g.,
difficulty of activity, time spent working, effort, responsibility, etc.)

IMPORTANCE OF CONVERSATI CNS

8 UBJE CT MATTE R

Personal Social Situational
Issues* Issues** Issues*** Other

tn Utmost
: Great
on Some
to Little
ta None

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Illlll

 

 

 

"1111111111?