CO NNECTIONS 19(1):43-57
©1996 INSNA
Embedding Subgroups in a Sociogram:
Linking Theory and Image 1
Kenneth A. Frank
M ichigan State University
Jeff Yasu m oto
University of Chicago
By em b ed d in g su b g r ou p s in a sociog r a m w e g en er a te im a g es con sisten t w ith lon g sta n d in g
th eo r etical d escr ip tio n s of n etw o r k str u ctu r e. M or eov er , th ese im a g es su sta in an eclectic ar r a y
o f th e o r etica lly b a sed in ter p r eta tio n s, th u s p r ov id in g a b a sis fo r th eor etica l in teg r a tio n . W e
g en er ate a n d in ter p r et tw o im a g es, on e of p r ofession a l d iscu ssion s am on g h ig h sch ool tea ch er s
a n d th e oth er of fr ien d sh ip s am o n g th e Fr en ch fin a n cia l elite. O u r fin d in g s su g g est th a t th is
a p p r oa ch h a s g r ea t p o ten tia l fo r in for m in g ch a ra cter iz ation s an d in ter p r eta tion s of th e str u ctu r e
o f v a r io u s socia l n etw o r k s.
1. Theoretical Images of the Structure of Social N etw orks
One of the strongest and m ost consistent theoretical im ages of the stru ctu re of social
netw orks is that of interactions concentrated w ithin, bu t not confined to, cohesive subgrou p s.
Su ch a d escription w as offered early by Roethlisberger and Dickson (1941) w ho stu d ied
w orkers w h o organized them selves into cliqu es w ithin a bank-w iring room , and has been
treated theoretically by Du rkheim in The Division of Labor in Society (1933), Sim m el in Conflict
and the W eb of Group A ffiliations (1955), and Blau in Inequality and Heterogeneity (1977), each of
w hom d escribed the integration of cohesive su bgrou p s into organizations or society throu gh
interactions w hich extend beyond subgrou p bou nd aries. This im age is also central to recent
theoretical ad van cem ents, su ch as the prim ary and second ary stru ctu ral holes w hich Bu rt
1
This paper contains portions of a paper presented at The Annual Meeting of the Classification Society
of North America, Houston Texas, June, 1994, and a paper to be published in Social Networks. The research
reported in this article was supported by a grant from the National Science Foundation and the National Center
for Educational Statistics (SES -8803225). The opinions expressed herein are those of the authors and not of the
sponsoring agencies.
W e thank Tony Bryk, Charles Bidwell, Betsy Becker, Nicole Ellefson, Phil Schuum, Kazuo
Yamaguchi and Benjamin Wright for their thoughtful comments on work related to this article. Thanks to Jan
De Leeuw for providing a Fortran version of Smacof (which later became ALSCAL). Thanks to Charles
Kadushin for providing data on the French financial elite and the much sought after book The Power Brokers.
Fortran routines from SLATEC, RANLIB, and CDFLIB were called in the Fortran program KliqueFinder.
Correspondence regarding this paper should be addressed to Ken Frank, Department of Counseling, Educational
Psychology and Special Education, Room 460 Erickson Hall, Michigan State University, East Lansing,
Michigan, 48824-1034. E-mail: [email protected].
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(1992) d efines using the theoretical im age show n in Figu re 1. Granovetter’s (1973) hyp othesis
regard ing strong ties (actors w ho are friend s w ith m any com m on others are inclined to interact
m ore frequ ently) also is consistent w ith an im age of d ense patterns of interactions concentrated
w ithin the bou nd aries of cohesive subgrou p s.
Fig u re 1. Th eo re tical Re p re s e n tatio n o f S u b g ro u p s Em b e d d ed in a S o cio g ram (Bu rt, 1992:95)
Unfortu nately, d ata analysts have not su ccessfully rep resented the pattern of observed
interactions am ong actors in a form that is consistent w ith theoretical d escrip tions. Some d ata
analysts have used Mu ltid im ensional Scaling (MDS), su ch as is perform ed by Krackp lot 2.0
(Krackhard t et. al. 1994), to rep resent the pattern of interaction am ong actors. While this
ap p roach rend ers an im age of actors located in a few d im ensions, it offers no objective basis
for id entifying those actors w ho are m em bers of a given subgrou p . It is left to the researcher
to use heu ristic and visu al criteria to id entify su bgrou p s of actors on a post-hoc basis.
Other d ata analysts have id entified blocks of stru cturally sim ilar actors, and relied on the
in form ation contained in the block d iagonal to rep resent the pattern of the social netw ork
(And erson et al., 1992; Borgatti and Everett, 1994; Bu rt, 1982; Doreian et al., 1994; Panning, 1982;
Snijd ers and N ow icki, 1994; Wasserm an and And erson, 1987; White et al. 1976). Although
recent ad aptations have rep resented the inform ation u sing shad ing instead of the nu m erical
inform ation contained in each cell (Freem an , 1994), the inform ation rem ains organized in
essentially the tabu lar form of an ad jacen cy m atrix instead of a grap hical im age su ch as is
generated by MDS.
Frank (1996) combined MDS and a sp ecial form of blockm od eling to generate an im age of
observed social netw ork d ata that is consistent w ith the theoretical d ep iction of in teractions
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concentrated w ithin su bgrou p s. In the next section w e w ill d iscu ss Frank’s stochastic d efinition
of cohesion w hich is key to Frank’s ability to id entify non-overlap p ing cohesive su bgrou p s. The
criterion is also the basis of th e tw o statistical tests Frank uses to evalu ate the salience of the
recovered su bgroup s. Once su ch su bgroup s have been id entified , w e extend trad itional MDS
by app lying it w ithin and betw een su bgroup s to generate an im age of the stru ctu re of social
netw ork d ata consistent w ith theoretical d escrip tion. In Section 3 w e generate and interp ret
an im age of the stru ctu re of professional d iscu ssions of teachers in a high school, and in Section
4 w e generate and interp ret an im age of patterns of friend ship am ong the fin an cial elite in
France (Kad u shin, 1995). In Section 5 w e d iscu ss the possibilities for the general ap p lication
of this ap p roach.
2. Identifying N on-overlapping Cohesive Subgroups
Frank (1995) d efined a stochastic criterion for id entifying cohesive su bgroup s from a
red u ced form of the p1 m od el (Fienberg and Wasserm an, 1981; Fienberg et al. 1985; Frank and
Strau ss, 1986; H olland and Leinhard t, 1981; Strau ss and Iked a, 1990; Wang and Wong, 1987;
Wasserm an and Galaskiew icz, 1984; Wasserm an & Pattison, 1994). Maxim izing Frank’s
criterion is equ ivalent to m axim izing the od d s ratio (AD/ CB) of Table 1.
The od d s ratio of Table 1 is large to the extent that actors interact w ith m em bers of their
su bgroup s (cell D) and d o not interact w ith m em bers of other su bgroup s (cell A). The od d s
ratio is sm all to the extent that actors d o not interact w ith m em bers of their su bgrou p s (cell C)
and actors interact w ith others w ho are not in their su bgrou p (cell B). Moreover, the od d s ratio
has the d irect interp retation as the od d s that tw o actors in the sam e su bgrou p w ill interact
relative to the od d s that tw o actors in d ifferent su bgrou p s w ill interact. Becau se the od d s ratio
is stochastic, w ith values on the d iagonals essentially evalu ated relative to the m arginals, the
od d s ratio accom m od ates variation in the d ata, and thu s allow s the researcher to id entify nonoverlap p ing, bu t p erm eable, subgroup bound aries instead of overlap p ing subgroup s of actors
satisfying a fixed criterion (m ost of the criteria available in UCIN ET and STRUCTURE are not
stochastic, and therefore generate overlap p ing su bgrou p s --see Frank, 1993, Freem an, 1992, and
Kad u shin, 1995). Given the stochastic criterion, Frank d escribed a sim p le hill-clim bing
algorithm for id entifying su bgroup s by iteratively reassigning actors so as to m axim ize the
od d s ratio of Table 1. Frank ap p lied the algorithm to d ata ind icating p rofessional d iscu ssions
(ranging from once a m onth [1] to d aily [4]) am ong teachers in a high school called “Ou r
H am ilton H igh”.
While the bou nd aries of the cohesive su bgrou p s m ay be the key comp onent of the
stru ctu ral rep resentation of the pattern of professional d iscu ssions, the placem ent of actors in
su bgrou p s constitu tes an incom p lete rep resentation of the d ata. Lost in the sim p le
categorization of actors into su bgroup s is the variability of patterns of in teractions am ong
actors w ith in each su bgrou p , and the variability in the extent and natu re of interactions in
w hich actors engage w ith others ou tsid e their su bgrou p s. Ou r Figu re 2 (and Frank’s Figu re 2)
rep resents the variability of the observed interactions by rep resenting all of the original d ata,
w hile sim u ltaneou sly su p p orting d ata red u ction by locating actors w ithin their cohesive
su bgrou p s. The su bgrou p s w ere em bed d ed in the sociogram by ap p lyin g MDS w ithin each
su bgroup to obtain the locations of su bgroup m em bers relative to one another, and then MDS
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betw een subgrou p s to obtain th e locations of subgrou p s relative to each another, and then
com bining the inform ation in a single im age.
Table 1.
Association Betw een Common Subgroup Membership and
The Realization of Interaction Betw een Actors
Interaction Realized
No
Yes
D ifferent
A
B
Possible interactions
betw een actors in
different su bgrou p s
Same
C
D
Possible interactions
betw een actors in the
same su bgrou p
Unrealized
interactions
Realized
interactions
Subgroup
Membership
Total possible
interactions
Before using the su bgrou p s as the basis for characterizing th e p attern of professional
d iscu ssions am ong these teachers, w e need to know the extent to w hich the interaction s are
concentrated w ithin the su bgrou p s at a rate that is unlikely to occu r by chance alone. That is,
w e m u st answ er the qu estion: “Are there really subgrou p s in the d ata, or have subgrou p s been
im p osed on a flu id p attern of interactions?” Frank (1996) d eterm ined that the probability that
the interactions w ere concentrated w ithin the su bgrou p s in Figure 2 at a rate that cou ld have
occu rred by chance alone is less than one in a thousand . Fu rther, Frank d eterm ined that the
algorithm w as likely to have recovered the “tru e” su bgroup m em bership s. In sim u lated d ata
in w hich the su bgrou p m em bership s w ere know n and in w h ich interactions w ere as
concentrated w ithin su bgroup s as they are in Figu re 2, Frank (1995) show ed that the algorithm
w as m ore than four tim es as likely to assign tw o actors w ho w ere in the sam e know n su bgroup
to the sam e observed su bgroup as it w as to assign tw o actors in d ifferent know n su bgroup s to
the sam e observed su bgroup . Thu s the su bgroup s of teachers represented in Figu re 2 are m ore
than bou nd aries im p osed to facilitate an analysis of a p attern of interactions — they represent
an em p irical tend ency of teachers to interact w ithin the id entified su bgrou p bou nd aries.
3. Interpreting the Image of Professional D iscussions in “Our Hamilton
High”
The im age in Figu re 2 reveals the basic stru ctu re of p rofessional d iscussions w ithin each
su bgrou p and betw een the subgrou p s. For exam p le, su bgrou p B can be characterized in term s
of a central d yad (teachers 20 and 23), tw o teachers closely associated w ith the d yad but w ho
d o not engage in d irect d iscu ssions w ith one another (teachers 17 and 22), and tw o perip heral
m em bers (teachers 6 and 8).
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Each of the su bgrou p s can be sim ilarly characterized , as can the stru ctu re of su bgrou p s, w hich
m ight be characterized in term s of a central su bgroup (C), a closely linked neighbor (su bgroup
D) and tw o p erip heral su bgroup s (A and B). Fu rther, becau se the m etric in the original d ata
is preserved w ithin and betw een su bgrou p s (see Frank, 1996 for a d iscu ssion of how the m etric
is preserved ), sets of d istances in the m ap can be com p ared . For exam p le, the m em bers of
su bgroup A are m ap p ed , on average, about 1.68 units ap art, reflecting the d ensity of
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d iscu ssions w ithin su bgrou p A of 2.42, or alm ost once a w eek (1.68=[Maxim u m
w eight]/ [d ensity w ithin subgrou p A]=4/ [2.42]). The average d istance of 1.68 betw een
m em bers of subgrou p A can be sensibly com p ared to the average d istance of 2.48 betw een
m em bers of su bgroup B w ho engaged in d iscu ssions on average about once a m onth
(2.48=[Maxim u m w eight]/ [d ensity w ithin su bgroup B]=4/ [1.6]). The d istances w ithin the
bou nd ary of su bgrou p A also can be com p ared w ith the d istances betw een m em bers of
d ifferent su bgroup s, su ch as the 16 units that sep arate the m em bers of su bgrou p s A and C 2.
Th e im age in Figu re 2 su stains an analysis of the stru ctu re of interactions at m any levels
and w ith resp ect to m any d ifferent theories precisely because it is consistent w ith theoretical
d escrip tions of the stru ctu re of interactions. The su bgrou p bou nd aries embed d ed in Figu re 2
reveal strong and w eak ties (Granovetter, 1973). Ties w hich occu r w ithin su bgrou p s, su ch as
w ithin su bgrou p A, are strong. They typically reflect a greater frequ ency of d iscu ssion and
typ ically occu r betw een tw o actors w ho engage in d iscussions w ith m any com m on others -the other m em bers of their su bgroup . Weak ties betw een su bgroup s are typ ically less frequ ent,
and occu r betw een actors w ho engage in interaction w ith few com m on others because they are
m em bers of d ifferent su bgrou p s.
The su bgrou p bou n d aries em bed d ed w ithin the im age in Figure 2 also reveal stru ctu ral
holes w ithin and betw een su bgrou p s (Bu rt, 1992) For exam p le, w ithin subgrou p C, the lim ited
am ou nt of d irect d iscu ssion betw een teachers 14 and 15 in the u p p er right and teachers 4 and
16 in the low er left constitu tes a stru ctu ral hole w ithin the su bgroup (only one of the four
p ossible interactions occu rs). This hole is filled prim arily by teachers 5, 10, and 19, each of
w h om engage in d irect d iscu ssion w ith three of the fou r d isconnected teachers. In Bu rt's
langu age, the action of teachers 5, 10, and 19 w ou ld be less constrained than that of teachers
4, 14, 15, and 16. There also are stru ctu ral holes betw een teachers in d ifferent su bgroup s. For
exam p le, there w ould be a h ole betw een su bgroup s A and B w ere it not for the connections
betw een actor 2 (of su bgroup A) and actor 17 (of su bgroup B) and teacher 1 (of su bgroup A)
and teachers 22 and 23 (of su bgrou p B).
The id entification of stru ctu ral holes can be generalized to d efine the p ositions of actors
in term s of their location in the im age (Freem an, 1992). For exam p le, in Figu re 2, teachers 20
and 23 occu p y sim ilarly central positions in su bgrou p B, and teachers 6 and 8 occu p y sim ilarly
p erip heral positions in su bgroup B. Fu rther, com p arisons of positions across su bgrou p s
op erationalize recent red efinitions of stru ctu ral sim ilarity in w hich tw o actors occu p y a sim ilar
p osition if the actors to whom they are related occup y stru ctu rally sim ilar p ositions. Fau st (1988)
refers to this as general equ ivalence and Borgatti and Everett (1994) characterize su ch
relationship s in term s of stru ctu ral isom orp hism s. Using Fau st’s term , teachers 20 and 23 w ho
are central to su bgrou p B m ay be characterized as generally equ ivalent w ith teachers 21 and
** w ho are central to subgrou p D. General equ ivalence also m ay be d efined relative to betw een
su bgroup d iscu ssions; teacher 13 in su bgroup D, w ho brid ges betw een teachers in su bgroup s
A and B, m ight be characterized as generally equ ivalent w ith teacher 3 in subgrou p C w ho d oes
the sam e. Therefore teachers 13 and 3 occup y sim ilar p ositions, even thou gh there are no d irect
and few ind irect (throu gh a single interm ed iary) interactions betw een them . The sim ilarity is
2
Distances in different images also could be compared to the extent that the weights in the original data
are measured on comparable scales and the metric is preserved in constructing the image.
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in the su bgrou p m em berships of those w ith w hom they engage in d iscu ssions ou tsid e of their
ow n su bgrou p .
In general, the internal stru ctu res of an organization, inclu d ing the stru ctu re of interaction,
w ill affect the w ay in w hich the entire organization resp ond s to external influ ences (Katz and
Kahn, 1966; Pfeffer and Salancik, 1978). At “Ou r H am ilton H igh,” the stu d ent popu lation has
becom e increasingly d isad vantaged over the years, as poor fam ilies have m oved to the d istrict
from a nearby city and as the child ren of the m ore established w ealthier fam ilies have aged .
The teach ers have resp ond ed in various w ays to this exogenous change. Som e w ho had
d ifficu lty ad ap ting to the change sought early retirem ent. Others altered their m od e of
interaction w ith the stu d ents, befriend ing the stu d ents w hom they felt w ere in the m ost need .
Bu t a core of teachers in the school have resp ond ed by becom ing “m oral agents,” incu lcating
stu d ents into a specific set of valu es emp hasizing citizenship and responsibility. These teachers
p u rsu e their goal by keeping firm control of the classroom and lead ing by exam p le. We used
the ranks of the teachers' m easu res on m oral agency as m easu red by responses to survey item s
(reliability=.74, see Frank, 1995, for a d escrip tion of the item s), as a basis for the teacher
id entification nu m bers in Figu re 2. The low er the ID nu m ber, the m ore the teacher em p hasized
m oral agency.
Unfortu nately, w e d id not obtain longitu d inal d ata to ad equ ately observe processes
through w hich teachers influ enced one another to create the organizational resp onses to the
change in stu d ent com p osition. This is often the case for those w ho stu d y the social netw orks
of organizations, and statistical techniqu es have been d evelop ed for estim ating the param eters
in m od els w hich are based on hypothesized p rocesses of influ ence, even thou gh the d ata are
only cross-sectional (e.g., Doreian, 1981; Fried kin and Marsd en, 1994). Sim ilarly, an im age of
in teractions can be interp reted w ith resp ect to a hypothetical cycle of influ ence that occurs
rep eated ly and continu ously. If w e assu m e the pattern of professional d iscu ssions to be
relatively stable (w hich is likely, given that m ost of the teachers have been in the school for
m ore than 15 years and have settled into a pattern of d iscussion w ith a fixed set of colleagu es),
w e can use the inform ation ind icating frequ ency of p rofessional d iscussions to constru ct a
hyp othetical pattern of influ ence in the school.
We begin d escribing the p rocess w ith the core of em p hasis on m oral agency, the m em bers
of su bgroup A (teachers 1, 2, 7, and 9). Moral agency is cu ltivated w ithin su bgroup A as the
teachers in su bgroup A engage in d iscu ssions w ith one another on a near d aily basis. Then one
of the teachers in su bgroup A engages in d iscu ssions w ith a teacher outsid e the su bgroup , thu s
p ossibly influ encing the m em ber of the other subgrou p . For exam p le, teacher 1 establishes her
em p hasis on m oral agency as she engages in professional d iscu ssions alm ost d aily w ith
teachers 2, 7, and 9 in her subgrou p . Occasionally (less than once a m onth) teacher 1 engages
in professional d iscu ssions w ith teacher 16 of subgroup C through w hich she m ay have som e
sm all influ ence on teacher 16 to em p hasize m oral agency m ore than he otherw ise w ou ld . In
tu rn, teacher 16 engages in d aily d iscu ssions w ith su bgrou p m em bers 3, 4, 5, 10, an d 19,
su p p orting the m od erate em p hasis on m oral agency in su bgrou p C. The professional
d iscu ssion betw een teachers 1 and 16 constitu tes a w eak tie, in that it occu rs infrequ ently and
betw een tw o teachers w ho have few others in com m on. Yet the effect of these d iscu ssions is
critical to integrating the subgrou p s into the totality of the organization, as op inions,
inform ation, etc., accu m u lated in each su bgroup d u ring a typical w eek are transm itted to
another subgrou p throu gh the w eak tie.
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The effect of cross-su bgroup d iscu ssions is not lim ited to those in subgroup C w ith w hom
teachers in su bgrou p A engage in d irect d iscu ssions. For exam p le, teacher 15 in su bgrou p C,
w ho engages in frequ ent d iscu ssions w ith teacher 1 in subgroup A, also engages in d iscu ssions
w ith teacher 18 in su bgrou p D, and likely influ ences teacher 18 to em p hasize m oral agency
m ore than he otherw ise w ou ld . Again, the effect is not lim ited to teacher 18 w ho then engages
in professional d iscu ssions w ith su bgroup m em bers 11 and **, and either influ ences them to
em p hasize, or su stains their em p hasis on (in the case of actor 11), m oral agency. Therefore
even teachers w ho d o not ad op t m oral agency in d irect response to changes in the stu d ent
p op u lation m ay be affected , throu gh d irect and ind irect in teractions, by the teachers in
su bgroup A w ho d o ad opt moral agency, although the effect is likely to be attenu ated w ith
each step in the process.
Of cou rse, teachers m ay experience the context of the school d ifferently d ep end ing on their
form al position in the school. For exam p le, the teachers in su bgrou p D, many of w hom teach
p hysical ed u cation, interact w ith a su bset of stu d ents in a non-acad em ic context, that of coach
and athlete. In these non-acad em ic contexts the coaches d evelop a personal relationship w ith
their stud ents, w hich Qu iroz et. al. (1991) d escribed as ind icative of the “p al” orientation (the
p al establishes a close p ersonal relationship w ith the stu d ent, characterized by sh aring
inform ation about personal lives outsid e of the classroom ). Like the teachers in su bgroup A
w ith regard to m oral agency, the teachers in su bgrou p D m ay reinforce each others’ em p hasis
on the pal orientation through their frequ ent d iscu ssions. Then w hen the teachers of su bgroup
D en gage in d iscu ssions outsid e their su bgroup they are likely to influ ence the m em bers of
other su bgrou p s tow ard s the pal orientation.
Alth ou gh th is d escrip tion of the processes of influ ence has been at the level of the
ind ivid u al teacher, a sim ilar d escrip tion can be su stained at the level of the school. For
exam p le, w e m ay d escribe m oral agency as being cu ltivated w ith in su bgrou p A and then
sp read ing to oth er su bgrou p s w here it encou nters the com p eting pal orientation w hich is
cu ltivated in su bgroup D. Ind eed , at the organizational level, the im age in Figu re 2 rep resents
an equ ilibrium of the system , w ith those in su bgrou p C w ho are m ixed and m od erate in their
orientations m ed iating betw een the com p eting orientations of those at the top and bottom .
It should not be su rp rising that the su bgroup bou nd aries are key to the sim u ltaneous
d escrip tion of in flu ence w ith regard to ind ivid u al contexts and organization processes. We
characterize the general natu re of influ ences of, and on, an ind ivid u al in term s of interactions
w ithin the su bgroup . We characterize organizational processes by referring to a host of
influ ences w ithin su bgrou p s and then the occasional betw een su bgrou p effect. Thu s the im age
in Figu re 2 reveals how effects at the level of ind ivid u al teachers in on e su bgroup becom e
“effects of the organization” as they are transm itted to teachers in another su bgrou p .
4. Application: Subgroups Among the French Financial Elite
Ou r d escription of influence w ithin and betw een cohesive su bgrou p s in Figu re 2 pertains
to d ata rep resenting professional d iscu ssions am ong essentially collegial actors -- teachers in
a single school -- and relates the pattern of d iscu ssion to the d istribu tion of orientations to
teaching. Bu t cohesive su bgrou p s also form the basis of other organizations, and m ay be
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d efined based on other typ es of social netw ork d ata. For exam p le, actors in highly politicized
grou p s (Pfeffer, 1982) su ch as the m em bers of Kad u shin’s French financial elite (1995) m ay be
organized into cohesive su bgroup s. H ere, th e su bgroup s establish the “ongoing system s of
social relations” (p .487) d escribed by Granovetter w hich create em bed d ed tru st. Com bining
Granovetter *s p ersp ectives w ith Bu rt’s theory of action, Kad u shin characterized the cond itions
w hich engend er enforceable trust, w hich
“cannot be an attribu te of friend sh ip p airs, nor is it d ed u cible from the possession of
com m on social attribu tes. Rather it stem s from an interw oven netw ork in w hich there
is a clear exp ectation th at actions w ill have positive and negative sanctions — not
necessarily from one *s im m ed iate friend s, bu t from a m ore d iffu se friend ship circle”
(page 219).
Kad u shin characterized these cond itions in term s of a com bination of stru ctu ral equ ivalence
and cohesion. These tw o m echanism s are effected throu gh the “interw oven netw ork,” w hich
w e contend is contained by the bou nd aries of the cohesive su bgroup . From the level of the
ind ivid u al, the others w ithin one’s su bgrou p w ith w hom one interacts are likely to be
associated throu gh d irect an d ind irect ties. It is these ties am ong su bgrou p m em bers w hich
constrain the actor. If th e ties are friend ships, then an actor w ho betrays a friend w ithin a
su bgroup w ill likely encounter negative sanctions as the effect reverberates throughout the
su bgrou p — the “d iffu se social circle.” Thu s tru st is enforced w ithin the su bgrou p . Becau se
there is no sim ilar stru ctu re through w hich actors can enforce th e tru st of non-su bgroup
m em bers, m em bers of d ifferent su bgrou p s m ay com p ete op enly and d irectly w ith one another,
even if there are a few friend ship ties w hich cu t across su bgrou p bou nd aries.
In ord er to reveal m ore fu lly th e stru ctu re throu gh w hich actors enforce tru st, w e have
generated an im age of the stru cture of unw eighted friend ship s am ong the French financial elite
w ithin and betw een su bgroup s in Figu re 3. Friend ship s w ere concentrated w ithin the
su bgrou p s at a rate that w ou ld have been fou nd in the id entified su bgrou p s less than one tim e
out of one thousand if the actors en gaged in friend ship s w ithout regard for subgroup
m em bership . That is, although as Kad u shin noted the d ensity is high am ong the financial elite
as a w hole, there is evid ence that the friend ship s are concentrated w ithin cohesive subgrou p s.
Fu rther the algorithm likely has recovered the tru e su bgroup m em bership s; in sim u lated d ata
w ith com p arable netw ork prop erties, the algorithm w as five tim es as likely to assign tw o actors
in the sam e know n su bgroup to the sam e observed su bgroup as tw o actors in d ifferent know n
su bgrou p s.
The representation of the entire friend ship netw ork in Figu re 3 as consisting of a series of
cohesive su bgrou p s w hich are loosely integrated into a w h ole is con sistent w ith Kad u shin’s
interp retation of the pattern of friend ships constitu ting a m oiety w h ich “d efines a system in
w hich the m em bers of the com m u nity ... are d ivid ed into tw o p arts w hich m aintain com p lex
relationship s varying from open hostility to very close intim acy, and w ith w hich various form s
of coop eration and rivalry are associated (Levi-Strau ss, 1969: 69).”
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In p articu lar, Kad u shin’s left moiety app ears at the top of ou r figu re and his right moiety
ap p ears at the bottom . Bu t the cohesive su bgroup s ind icate the basis of enforceable tru st m ore
so than the left versu s right d ichotom y of Kad u sh in ’s im age. First, actors share com m on
socializing exp eriences m ostly w ith m em bers of their su bgrou p s. Follow ing Kad u shin, w e
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53
includ e inform ation regard ing party m em bership (Soc=Socialist, Cen=Central, Rgt=Right, and
N on=N one, or unknow n) and w hether or not the actor w as a grad u ate of EN A as ind icated by
an “E”. In ad d ition, w e inclu d e other characteristics of the actors w hich w e fou nd to be related
to the stru ctu re of friend ship (som e of this inform ation w as obtained from De Qu illacq, 1993).
We ind icate w hich actors w ere m em bers of Résistance d u Socialism e (an antisocialist
organization) by inclu d ing an “R” in the actor *s line of inform ation, w hich actors w ere bankers
by inclu d in g a “B”, w hich actors w ere m em bers of the treasu ry by inclu d ing a “T”, w hich
actors w ere partners in the prestigiou s financial ad visory firm Firm e d e la Finance w ith an “F”,
and w hich m em bers w ere associated w ith Grand e Banqu e w ith the letter “G.”
Becau se the subgrou p s are consistent w ith Kad u shin *s m oiety, it is not su rp rising that party
affiliation and grad u ation from EN A are related to subgrou p m em bership , bu t the alignm ent
of party m em bership , ed u cation and friend ship are clearer in ou r Figu re 3 than in Kad u shin’s
Figu re 1 (p age 211). The m ajority of actors in su bgrou p A are socialists, all of w hom grad u ated
from EN A. Su bgrou p B is anchored by three partners from Firm e d e la Finance (actors 10, 17,
and 6) and others w ho are d irectly linked to them throu gh activities in the financial ad vising
and banking ind u stries. Most of th e m em bers in su bgrou p C have particip ated in the soap
op era involved in changing chairm anship s and board m em bership s of Grand e Banqu e. Three
of the m em bers of su bgroup D w ere ap p ointed by one conservative prim e m inister, and the
fou rth, actor 23, by another conservative prim e m inister.
There are enough comm onalities betw een actors of d ifferent su bgroup s to integrate the
w hole into a m oiety. For exam p le, the basis of the brid ges betw een the m em bers of Su bgroup
A and the m em bers of subgrou p D w ere form ed d u ring attend ance at EN A and em p loym ent
at the treasury. Also, there are ties based on party m em bership betw een m em bers of su bgroup
A and m em bers of su bgrou p C. Actors 24 and 26, tw o of the socialists in su bgrou p A, are
friend s w ith the lone socialist in su bgroup C, actor 1 (although actor 1's comm itm ent to
socialism is not as strong as that of m any of the actors in su bgroup A), and actor 12 of su bgroup
A, one of the few m em bers of the right in su bgroup A, is friend s w ith a stau nch su p p orter of
the right in su bgroup C, actor 4. These ties w hich sp an across su bgroup s allow the socialists
w ho are central in su bgrou p A to establish them selves as m ed iators betw een those affiliated
w ith the Grand e Banqu e in su bgroup C and the m ore ad vantaged m em bers (in term s of
attend ing EN A) of the right in su bgroup D. Perhap s the role w as established w hen the
socialists w ere in pow er and ad op ted the pragm atic rou te of privatizing ind u stry, requ iring
them to d raw on com m onalities w ith m em bers of other su bgrou p s of varying econom ic
ad vantage and politics. This interp retation w ould be consistent w ith the brid ges betw een the
m em bers of su bgrou p s A and B, m any of w hich have a basis in em p loym ent in th e banking
ind u stry.
The com m onalities w ithin su bgrou p s provid e a basis for th e n orm s w hich ap p ly to each
su bgroup . For exam p le, the actors in su bgroup D are united by their comm itm ent to
conservative principles su ch as privatization of ind u stries and banks, w hile the m em bers in
su bgrou p A, except for actor 12, are com m itted to the nationalization of ind u stry and banks,
and are relu ctant to enter into the comm on Eu ropean comm u nity. Fu rther, m an y of the
m em bers of su bgroup A w ere socialized by exp eriences in the treasury, w ith its repu tation for,
and em p hasis on, technical p row ess. Althou gh the actors in su bgrou p C are on ly loosely
connected and the com m on association w ith the Grand e Banqu e soap op era h as prod u ced
54
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som e anim osities, they share com m on und erstand ings abou t the ru les of takeovers and ou sters,
m anip u lating events throu gh board m em bership s and back room influ ence.
While the p rior exp eriences of the m em bers of each su bgroup provid e the basis for
establishing the norm s and m ores of the su bgrou p , it is the d ense friend ship patterns w ithin
su bgrou p s, especially subgrou p s A and B, w hich establish the stru ctu re throu gh w hich tru st
is enforced . In Bu rt’s (1992) term s, the actions of those ind ivid u als w ho are closely tied to a set
of actors w ho are m em bers of a single su bgroup are constrained . In their d ealings w ith one
another they m u st conform to the su bgrou p norm s, for to violate the su bgrou p norm m ay resu lt
not only in the loss of a specific friend , bu t m ay bring negative sanctions am ong the circle of
friend s d efined by the su bgrou p . For exam p le, the cap acity for friend ship of actor 26 in
su bgrou p A an d actor 17 in su bgrou p B places them in the m id d le of fairly d ensely knit
su bgrou p s. Given their location in the netw ork structu re, one m ight assu m e that they w ere
highly influ ential. On the contrary, their behavior is constrained by th e h ost of others w ith
w hom they are friend s. To d eal aggressively w ith a m em ber of their ow n su bgrou p m ay resu lt
in the loss of several friend ship s, w hich w ould be p articu larly d ifficu lt p ersonally for these tw o
actors w ho are d escribed as “too nice” or “too social” to be highly influ ential (these actors have
ID’s am ong the highest in the grou p becau se w e assigned ID’s accord ing to the extent to w hich
the actor’s w ere d escribed as influ ential by other m em bers of the group — the low er the ID, the
m ore influ ence the actor has 3).
The constraints on actors 17 and 26 as a resu lt of th eir centrality in cohesive su bgroup s
represents the effect of enforceable tru st d escribed by Kad u shin and Granovetter. At the level
of the su bgrou p , this illu m inates Granovetter’s (1973) and Kad u shin’s (1995) argu m ent w hich
d escribes enforceable tru st as occu rring am ong actors w ho are located in a com p lex w eb of
interactions am on g actors w ho share a norm ative environm ent. Although the comm onality
of actors lies p artly in their stru ctu ral equ ivalence, it is d ifficu lt to observe the com m onalities
in Kad u shin’s figu re in w hich actors are segregated into stru ctu rally sim ilar blocks. In our
figu re, the w hole of the phenom enon is cap tu red by the cohesive su bgrou p . Actors 17 and 26
are constrained by their p attern of friend ship s because, not only are they d irectly connected to
their friend s, bu t they occu p y stru ctu rally sim ilar positions as their friend s; e.g., the friend s of
actor 26 are them selves friend s. Thu s a cohesive su bgroup , althou gh d efin ed by a criterion
w hich em p hasizes d irect conn ections w ithin the su bgrou p , contains a set of actors w ho are
d irectly connected and stru ctu rally sim ilar by virtu e of their interacting w ith com m on others
w ithin the su bgrou p . It is these com p ou nd ed processes w hich d efine the stru ctu re throu gh
w hich tru st is enforced .
In contrast to actors 17 and 26, w ho are highly central to their subgrou p s bu t n ot very
influ ential in the netw ork, stand s actor 1 (of su bgrou p C) w ho is only loosely tied to his or any
su bgroup and is the m ost influ ential in the netw ork. This has provid ed him the freed om to
d eal aggressively w ith subgrou p m em bers such as actor 22 (also of subgrou p C) w hom he kept
from control of Grand e Banqu e. Given the cross-sectional natu re of the d ata one can interp ret
actor 1's actions tw o w ays. First, actor 1 had the freed om to d eal aggressively w ith actor 22
becau se actor 1 w ou ld experience little loss of friend ship as a resu lt of th e conflict (the only
3
O n ly th e relativ e in flu en ce o f actors 1 th rou g h 20 w e re kn ow n . Th e ID ’s of a ctors 21 th rou g h
28 w er e assig n ed r a n d o m ly .
E M BED D IN G S U BG RO U P S IN
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55
friend ship actor 1 has in this subgroup is w ith actor 28, w hom actor 1 help ed install as head of
a bank rival to Grand e Banqu e). On the other hand , perhap s actor 1 had m ore friend s w ithin
su bgrou p C prior to his d ealings w ith actor 22, and th e d ata reflect this loss of friend ship,
w hich actor 1 w as ap parently w illing to risk for his action of op p osing actor 22 . There is no
ind ication of any falling ou t betw een actor 1 and other m em bers of su bgroup C, and so the d ata
su p p ort the first exp lanation. Bu t either exp lanation is consistent w ith the argum ent that
cohesion w ithin su bgrou p s form s the basis of enforceable tru st. There w as no recourse for
actor 22 w hen he w as not su p p orted by actor 1. Any negative effects w hich he cou ld have
created in actor 1's friend ship netw ork either d id not exist or w ere exp end able from actor 1's
p ersp ective 4.
The effects of enforceable tru st can be d escribed at the level of the su bgrou p , as there w as
little conflict w ithin the most d ensely knit su bgrou p s. In fact, the only rep orted d irect conflict
w ithin su bgroup A occu rred w hen actor 12, now d esignated as a m em ber of the right, and the
socialist actor 24 stop p ed talking d u ring actor 12's ap p ointm ent by a conservative prim e
m inister. Most interestingly, this friend ship w as resu m ed w hen pow er changed hand s and
actor 12 w as no longer the ap p ointee of a conservative p olitician. Perhap s this w as facilitated
by actors 25 and 26 w ho are both friend s of actors 12 and 24. The only rep orted conflict
betw een actors in su bgrou p B occu rred w hen actor 10 resisted the p u sh actor 6 m ad e for his
son-in-law to becom e a partner in Firm e d e la Finance. This w as not a d irect conflict betw een
the tw o, as it concerned a third party, an d th ere are ind ications actor 17 has played an
im p ortant role in m aintaining the cohesiveness of the su bgrou p . Moreover, this event occu rred
recently, and the d iagram of friend ship s m ay not fu lly reflect the consequ ences of this event.
Tim e w ill tell if the conflict betw een actors 6 and 10 is great enough to d ivid e the su bgroup .
On the other hand , there are several exam p les of conflict am ong m em bers of loosely knit
su bgroup s C and D, and betw een m em bers of d ifferent su bgroup s. Actor 9 (of su bgroup A)
strongly resents actor 1 (of subgrou p C) w ho op p osed actor 9 as the head of Grand e Banqu e.
The lack of enforceable trust app lies as m u ch to actor 9, w hose resentm ent no one attem p ts to
m ed iate, as w ell as to actor 1, w ho exp erienced few repercu ssions as a resu lt of his opp osition
to actor 9. Actor 3's bid for actor 5's bank also represented conflict betw een su bgroup s
(su bgroup s D and B resp ectively), as d id actor 23's bid to m erge w ith the bank head ed by actor
28 (a conflict betw een a m em ber of su bgrou p D and a m em ber of subgrou p C). By far th e
d eepest an d m ost end u ring anim osities ru n betw een subgrou p s becau se there are few
m echanism s for enforcing tru st or m ed iating relationship s betw een m em bers of d ifferent
su bgroup s. Thus the location of friend ship s w ithin an d betw een su bgroup s help s us to
u nd erstand the sp ecific m echanism s throu gh w h ich tru st is enforced am ong the French
financial elite.
4
Other actors occupy positions similar to actor 1's, and are similarly unconstrained in their actions.
Actors 4 (of subgroup C) and 3 (of subgroup D) also are relatively unconstrained by enforceable trust, and they
take advantage of their position to engage in aggressive dealings (bidding for companies, take-overs, ousters)
with other actors in the network, with few personal repercussions.
56
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5. The General Value of Embedding Subgroups in a Sociogram
We have revealed th e stru ctu res of tw o very d ifferent social netw orks. The im age of
p rofessional d iscu ssions am ong teachers in “Ou r H am ilton H igh” help ed us to exp lore the
stru ctu re through w hich teachers influ enced each other’s ap p roach to teaching. The im age of
friend ship patterns am ong th e Fren ch financial elite help ed us to specify the m echanism
throu gh w hich actors enforced the tru st of other actors. Fu rther, each im age sustained a
d escrip tion of the processes at the level of the ind ivid u al and the group as a w hole; the
su bgroup s d efine the context for ind ivid u als and cap tu re processes w hich form the backbone
of a group or organization. Visu ally, subgroup s are the key to generalizing a set of interactions
in the sociogram m aking it possible to d escribe effects on actors of m em bers of a given
su bgrou p , and effects of subgrou p s on one another. The visu al representation is consistent
w ith theoretical d escriptions of su bgrou p s linking ind ivid u al and organization as ind ivid u als
influ ence one another through d irect interactions w ithin the su bgroup , and then integrate into
the larger organization throu gh interactions ou tsid e of the su bgrou p (Granovetter, 1973; N ad el,
1957; Sim m el, 1955).
The techniques d em onstrated in this article hold great p otential for characterizing the
stru ctu re of other social netw orks 5. The extent to w hich the potential w ill be realized w ill
d epend on several factors. The d efinition of a cohesive subgrou p alm ost inherently assum es
that the d ata are not d irected . Actors influence each other throu gh d iscu ssions, and tru st is
enforced throu gh friend ship s, both of w hich are m u tu al ties. For d irected d ata, perhaps it m ay
be more sensible to first categorize actors into stru ctu rally sim ilar blocks instead of cohesive
su bgroup s, although to the extent that blocks are stru cturally equ ivalent and not cohesive the
interp retation of su ch figu res w ill not ben efit from the generalization of processes w ithin
su bgroup s (see Frank 1996 for the d ifficu lty in interp reting figu res based on blocks of
stru ctu rally sim ilar actors).
Most im p ortantly, th e in terp retation of im ages of netw ork stru ctu res w ill d ep end on
theoretical d escrip tions of processes related to the su bstance of the social netw ork d ata. We
interp ret Figu re 2 in term s of influ ence, and Figu re 3 in term s of enforceable trust. While the
m ethod s for generating the sociogram s m ay be ap p lied across m an y d iscip lines, the
interp retations of the figu res, w ill, of cou rse, be d iscipline d ep end ent. Figu res rep resenting
econom ic exchange m ay be interp reted using theories of rational action. Figu res rep resenting
p olitical su p p ort m ay be interp reted accord ing to gam e theory. And yet the representation of
social netw orks in ou r figu res has allow ed us to integrate com p onents from seem ingly eclectic
theories. Our im ages reveal rep resentations of strong and w eak ties, stru ctu ral holes, and
p rocesses at ind ivid u al and grou p levels. We hop e that broad er app lications w ill reveal
comm onalities in theories of several d iscip lines even as each set of d ata is interp reted using the
p red om inant theories of the m ost relevant d iscip lines.
5
W e a r e w o r k in g w ith Stev e Bo r g a tti to in co r p o r a te th e clu ster in g p r o g r a m Kliqu eFin der a n d
th e tech n iq u es fo r co n str u ctin g th e M D S-b a sed im a g es in to th e n ext v er sion of U C IN ET in or d er to
m a k e th e ap p r o a ch d escr ib ed in th is ar ticle m or e accessib le.
57
References
Bu rt, R. 1983. “Distingu ishing Relational Contents” in A pplied N etwork A nalysis ed ited by R.
Bu rt and M. Minor. Beverly H ills, CA: Sage Publications.
Bu rt, R. 1984. “N etw ork Item s and the General Social Su rvey.” Social N etworks 6:293-339.
Brew er, D. 1995. "N o Associative Biases in the First N am e Cued Recall Proced u re for Eliciting
Personal N etw orks." Presented at the m eetings of the International N etw ork for Social
N etw ork Analysis in Lond on, England , Ju ly 1995.
Erickson, B.H . 1981. "N etw ork Sam p ling in Practice: Som e Secon d Step s." Social N etworks
3:127-136.
Fischer, C.S. 1982. "What Do We Mean by 'Friend '?: an Ind u ctive Stu d y." Social N etworks
3:287-306.
Fried kin, N . 1980. "A Test of the Stru ctu ral Featu res of Granovetter's Strength of Weak Ties
Theory." Social N etworks 2:411-422.
Killw orth, P., C. McCarty, E.C. Johnsen, G.A. Shelley, H .R. Bernard . 1995. “A Social N etw ork
Ap p roach to Estim ating Serop revalence in the United States.” Pap er und er review .
Lau m ann, E.O., J.H . Gagnon, S. Michaels, R.T. Michael, L.P. Schu m m . 1993. “Monitoring AIDS
and Other Rare Pop u lation Events: A N etw ork App roach.” Journal of Health and Social
Behavior 34:7-22.
McCallister, L. and C.S. Fischer. 1978 “A Proced u re for Su rveying Social N etw orks.”
Sociological M ethods and Research 7: 131-148.
Mitchell, J.C. 1969. “The Concep t and Use of Social Netw orks” in Social N etworks in Urban
Situations ed ited by J.C. Mitchell. Manchester, UK: Manchester University Press.
Mitchell, J.C. 1987. "The Com p onents of Strong Ties Am ong H om eless Wom en." Social
N etworks 9:37-47.
Pu ckett, N .N . 1975. Black N ames in A merica: Origins and Usage. Boston, G.K. H all.
Wellm an, B. 1979. "The Com m u nity Qu estion: The Intim ate N etw orks of East Yorkers."
A merican Journal of Sociology 84:1201-1231.