Du bach, I. N.; Pa ke , H.
A icle
An analysis o co po a e boa d ne wo ks in Sou h A ica
Sou h A ican Jou nal o Business Managemen
P o ided in Coope a ion wi h:
Uni e si y o S ellenbosch Business School (USB), Bell ille, Sou h A ica
Sugges ed Ci a ion: Du bach, I. N.; Pa ke , H. (2009) : An analysis o co po a e boa d ne wo ks in
Sou h A ica, Sou h A ican Jou nal o Business Managemen , ISSN 2078-5976, A ican Online
Scien i ic In o ma ion Sys ems (AOSIS), Cape Town, Vol. 40, Iss. 2, pp. 15-26,
h ps://doi.o g/10.4102/sajbm. 40i2.537
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/218416
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h ps://c ea i ecommons.o g/licenses/by/4.0/
S.A .J.Bus.Manage.2009,40(2) 15
An analysis o co po a e boa d ne wo ks in Sou h A ica
I.N. Du bach
Depa men o S a is ical Sciences, Uni e si y o Cape Town,
P i a e Bag, Rondebosch 7701, Republic o Sou h A ica
[email p o ec ed]c.za
H. Pa ke
G adua e School o Business, Uni e si y o Cape Town,
P i a e Bag, Rondebosch 7701, Republic o Sou h A ica
[email p o ec ed].ac.za
Recei ed Ap il 2009
In his pape we analyse he ne wo ks c ea ed om di ec o s si ing on he boa ds o companies in Sou h A ica. We
conside wo p ojec ions o his ne wo k: a di ec o ne wo k, in which only di ec o s a e p esen and wo di ec o s a e
linked i hey si oge he on one o mo e common boa ds; and a i m ne wo k, in which only i ms a e p esen and an
edge indica es ha he wo i ms sha e one o mo e di ec o s. We desc ibe hese ne wo ks in e ms o he s a is ical
p ope ies ha hey possess, and compa e hem o heo e ical alues ob ained unde a ious andom ne wo k models. The
ne wo k analysis is he i s o be applied o a ela i ely small eme ging economy like Sou h A ica. We ind ha many o
he ea u es p e iously ound o hold o highly-de eloped coun ies also apply he e, sugges ing ha co po a e ne wo ks
may be ai ly obus o s ages o economic de elopmen .
*To whom all co espondence should be add essed.
In oduc ion
Boa ds o di ec o s ha e been he ocus o much esea ch in
he managemen sciences. Possible easons o his in e es
a e no ha d o disce n. Fi s ly, he di ec o s si ing on he
boa d o a i m a e in a posi ion o exe cise a leas some
con ol o e he s a egic di ec ion aken by he i m, so ha
by s udying boa ds o di ec o s we hope o gain some
insigh in o he easons o he di e ences and simila i ies
we obse e in co po a e s a egy, and hus be e unde s and
he co po a e wo ld as a whole. Secondly, boa ds o
di ec o s o en o e lap wi h one ano he , whe e e a boa d
membe a ilia ed wi h one i m si s on he boa d o
di ec o s o ano he i m. Fi ms ha ing one o mo e
di ec o s in common a e ‘in e locked’, and he ne wo k
c ea ed by many such in e locking di ec o a es o e s ‘a
po en medium o he sp ead o co po a e p ac ice and
s uc u es’ (Da is, Yoo & Bake , 2003). Mo eo e , o
publicly aded i ms a leas , in o ma ion on boa d
membe ship is abundan , eliable and eadily a ailable, so
ha i is possible o econs uc he comple e ne wo k o
i ms and hei in e - ela ionships, and so gain a bi d’s-eye
iew o he en i e co po a e landscape.
In ecen imes, he analysis o he ypes o la ge and
complex ne wo ks exempli ied by a ne wo k o i ms has
ecei ed an eno mous amoun o a en ion (see Newman
(2003) o an o e iew). A ne wo k is simply a g aph in
which a se o nodes (o e ices) a e linked oge he by
edges. The nodes ep esen en i ies o some so , and he
edges indica e he p esence o some kind ela ionship o ie
be ween wo nodes. Fo example, i m ne wo ks a e
cons uc ed by conside ing i ms as nodes, wi h an edge
be ween i ms ep esen ing an in e lock be ween hose wo
i ms i.e. he p esence o one o mo e common di ec o s on
bo h he boa ds. F om his ela i ely simple empi ical da a, a
conside able amoun o in o ma ion on he agg ega e
s uc u e o he sys em can be de i ed using he
ma hema ical machine y de eloped o he analysis o hese
ne wo ks. This kind o ne wo k analysis has been used o
in es iga e a di e se a ay o complex sys ems, some
examples o which a e iendships be ween indi iduals
(Rapopo , 1961), con ac be ween sexual pa ne s (Jones &
Handcock, 2003), co-au ho ship o scien i ic pape s
(Newman, 2001), he s uc u e o he In e ne and
wo ldwide web (Ba abasi, Albe & Jeong, 2000), p eda o -
p ey ela ionships in ecological ood webs (Mon oya, Pimm
& Sole, 2006), he me abolic sys em o E.coli (Wagne ,
2001) and he co-occu ences o wo ds in human language
(Fe e i Cancho & Sole, 2001).
In his pape , we cons uc and analyse he ne wo k
desc ibing he cu en co po a e landscape in Sou h A ica.
We do his using in o ma ion on he boa ds o di ec o s o
all publicly-lis ed companies on he Johannesbu g S ock
Exchange (JSE) a 1 Ma ch 2008. Simila analyses ha e
been conduc ed o se e al o he coun ies, speci ically he
US (Newman, S oga z & Wa s, 2001, Da is e al., 2003,
Conyon & Muldoon, 2006), UK (Conyon & Muldoon,
2006), Ge many (Conyon & Muldoon, 2006; Kogu &
16 S.A .J.Bus.Manage.2009,40(2)
Belinky, 2008), Swi ze land and he Ne he lands
(Heemske k & Schnyde , 2008), and Denma k, Sweden and
No way (Sinani e al., 2008). Ou b oad aim in his pape is
o p o ide a simila o e iew o he co po a e ne wo k o
Sou h A ica, an eme ging ma ke di e ing om he mo e
highly-de eloped economies o he coun ies men ioned
abo e. In doing so, we show ha many o he s uc u al
ea u es ound o ne wo ks in o he coun ies also hold in
Sou h A ica, which sugges s ha hese co po a e ne wo ks
may be ela i ely insensi i e o he s ages o economic
de elopmen o a na ion.
The pape is s uc u ed as ollows. The i s wo sec ions
gi e an in oduc ion o he analysis o complex ne wo ks. A
summa y o p e ious esea ch on co po a e ne wo ks is hen
p o ided. We hen desc ibe he da a se used in he cu en
s udy, p o ide he esul s o he ne wo k analysis, and
compa e he esul s ob ained o hose p e iously ound o
o he coun ies. A inal sec ion o e s some conclusions and
ideas o u u e esea ch.
Rep esen ing boa ds o di ec o s wi h social
ne wo ks
A ne wo k is a g aph in which a se o nodes (o e ices)
a e linked oge he by edges. The nodes ep esen en i ies o
some so , and he edges indica e he p esence o some kind
ela ionship o ie be ween wo nodes. Fo example, when
examining boa ds o di ec o s he di ec o s hemsel es can
be hough o as nodes in he g aph, wi h an edge exis ing
be ween wo di ec o s i hey si oge he on he boa d o he
same company. An example o such a “di ec o -cen ic”
ne wo k is shown in Figu e 1, which shows he ne wo k ha
exis s be ween di ec o s o h ee o he i ms in ou cu en
s udy ( om le o igh as hey appea in Figu e 1: Ideco,
Simme and Jack Mines, and Fi s U anium Co po a ion).
Indi iduals ha si on mo e han one boa d a e deno ed by
black ci cles.
Figu e 1: Example o a di ec o ship ne wo k
I is also possible o iew co po a e di ec o ships in a
di e en way, by conside ing i ms o be he nodes o he
g aph wi h an edge exis ing be ween wo i ms i hey ha e
one o mo e boa d membe s in common. An example o his
kind o “ i m-cen ic” ne wo k is shown in Figu e 2, which
shows he ne wo k exis ing be ween he h ee i ms o
Figu e 1. Ideco and Simme and Jack Mines sha e one
di ec o (A Sisulu) and a e hus connec ed, while Simme
and Jack Mines and Fi s U anium Co po a ion sha e wo (G
Mille and N B une e) and a e hus also connec ed. No e
ha he e is some loss o in o ma ion he e: he i m-cen ic
ne wo k does no dis inguish be ween a pai o i ms ha
sha es one di ec o , and a pai ha sha es mo e han one
di ec o ( he same would be ue o he di ec o -cen ic
ne wo k in Figu e 1).
Figu e 2: Example o a i m ne wo k
The dual ep esen a ion o he co po a e di ec o ship
in o ma ion a ises because he e a e wo dis inc ypes o
nodes: di ec o s and i ms. A mo e succinc way o
ep esen ing co po a e di ec o ships is o ha e bo h di ec o
nodes and i m nodes in he same g aph, wi h an edge
be ween a di ec o and a i m i he di ec o is a boa d
membe o he i m. Thus, edges can only exis be ween
nodes o di e en ypes, ne e be ween wo di ec o s o wo
i ms. A ne wo k o his ype is called a bipa i e ne wo k.
The bipa i e ne wo k o he h ee- i m example is shown in
Figu e 3.
Figu e 3: Example o a bipa i e ne wo k o di ec o s
and i ms
The bipa i e g aph shows he ull s uc u e o he co po a e
di ec o ship ne wo k. No e ha he di ec o -cen ic and
i m-cen ic ne wo ks can be easily ob ained om he
bipa i e g aph. Fo example, by no ing ha Fi s U anium
Co po a ion and Simme and Jack Mines sha e wo
di ec o s, a link be ween hose wo i ms in he i m-cen ic
ne wo k can be in e ed. Figu e 3 also shows ha Fi s
U anium Co po a ion and Ideco ha e no di ec o s in
common – so ha he e would be no link be ween he i ms
in he i m-cen ic ne wo k. Simila obse a ions can be
made o ela ionships be ween di ec o s. In ne wo k e ms,
Figu e 1 shows he p ojec ion o he bipa i e g aph on o he
di ec o nodes (o di ec o p ojec ion o sho ), while Figu e
2 shows he p ojec ion o he bipa i e g aph on o he i m
nodes (o i m p ojec ion). In analysing he bipa i e g aphs
ep esen ing boa d membe ship, i is common o analyse he
wo p ojec ions sepa a ely – his is he app oach ha we ake
he e.
Cha ac e ising co po a e di ec o ship ne wo ks
Analysing social ne wo ks is la gely an exe cise in inding
app op ia e ways o ep esen ing he mos impo an
s uc u al aspec s o he ne wo k. When analysing ne wo ks
o di ec o s and i ms, he mos impo an s uc u al
ques ions o en ela e o how well “connec ed” he ne wo k
is. This connec edness is ypically measu ed using he
ollowing ne wo k measu es.
S.A .J.Bus.Manage.2009,40(2) 17
Size o he la ges connec ed componen
A connec ed componen associa ed wi h a pa icula node is
he collec ion o all nodes ha can be eached om ha
node by a elling along edges o he g aph. Fo example,
he ne wo k in Figu e 1 consis s o a single connec ed
componen since any node can be eached om any o he
node. Many ne wo ks, including he one we shall conside ,
ha e mo e han one connec ed componen . In hese cases,
he size o he la ges connec ed componen in he ne wo k
is usually gi en as an indica ion o he o e all
connec edness o he ne wo k. Nodes ha do no o m pa
o he la ges connec ed componen a e essen ially
pe iphe al o any dynamics occu ing wi hin he ne wo k.
Deg ee
The deg ee o a node is simply he numbe o edges lea ing
ha node and is he e o e an indica ion o how well-
connec ed a pa icula node is. A an agg ega e le el, he
a e age deg ee in a ne wo k p o ides an indica ion o he
a e age numbe o connec ions possessed by di ec o s o
i ms. Because he dis ibu ion o deg ee is usually s ongly
skewed o he igh , especially o he di ec o p ojec ion, i
is common o examine he ull deg ee dis ibu ion in
addi ion o summa ies such as he mean.
Dis ance
The dis ance be ween any wo nodes is he smalles numbe
o edges in he g aph ha mus be a e sed o each one
node om he o he . I ep esen s he leng h o he sho es
pa h be ween he wo nodes and can also be used as a p oxy
o how easily in o ma ion can sp ead be ween hese nodes
(o how easily in luence can be wielded, e c). Fo example,
di ec o s sepa a ed by a dis ance o one si on he same
boa d and a e hus in di ec con ac wi h one ano he .
Di ec o s ha a e sepa a ed by a dis ance o wo do no si
on he same boa d hemsel es, bu each si on hei
espec i e boa ds wi h a membe who is common o bo h o
he boa ds. They a e hus in indi ec con ac ia an
in e media y. As o deg ee, dis ances can be e alua ed by
aking he a e age dis ance o e all pai s o nodes o by
examining he ull dis ibu ion o dis ances. Whe e wo
nodes do no lie in he same connec ed componen , he e
exis s no pa h be ween hem and he dis ance be ween hem
is unde ined. As a esul , i is usual when compu ing he
a e age dis ance o conside only hose nodes ha lie in he
la ges connec ed componen .
Clus e ing
A highly-clus e ed ne wo k is one in which a node’s
neighbou s ( hose nodes o whom i is connec ed) end also
o be neighbou s hemsel es ( o also be connec ed o one
ano he ). Se e al de ini ions o he clus e ing coe icien
ha e been p oposed. One idea is o assess he o al numbe
o edges ha could exis be ween he neighbou s o a
pa icula node. I a node j has deg ee dj (implying ha i has
dj neighbou s) hen he e can be a mos dj(dj – 1)/2 edges
be ween hese dj neighbou s. The clus e ing coe icien o
node j is hen gi en by he p opo ion o hese edges ha
ac ually do exis in he g aph. An o e all clus e ing
coe icien can be ob ained by a e aging he clus e ing
coe icien s o all nodes in he ne wo k. We e e o his
measu e, ollowing Conyon and Muldoon (2006), as he
Wa s-S oga z clus e ing measu e, a e i s use in Wa s
(1999). An al e na e de ini ion uses a connec ed iple as he
uni o analysis. A connec ed iple is a se o h ee nodes,
say a, b, c, in which a is connec ed o b and b is connec ed
o c, bu a is no necessa ily connec ed o c. The p opo ion
o all connec ed iples in which a in ac is connec ed o c is
de ined as he ansi i i y-based clus e ing coe icien . Fo
example, he g aph in Figu e 2 shows a connec ed iple in
which he hi d link be ween Ideco and Fi s U anium
Co po a ion is no p esen . This g aph he e o e has a
clus e ing coe icien o 0, since he only connec ed iple is
no a comple ed iangle. Di ec o p ojec ions (and social
ne wo ks in gene al) end o show high clus e ing, because
he na u e o boa d membe ship is such ha i wo people
a e bo h connec ed o a hi d di ec o , i is p obably because
all h ee o hem si on he same boa d.
Asso a i i y
The no ion o asso a i e mixing explo es he co ela ion
be ween ce ain cha ac e is ics o nodes in a ne wo k and he
same cha ac e is ics o he nodes ha hey a e connec ed o.
A simple example is a social ne wo k whe e wo nodes a e
connec ed i hey a e ma ied o one ano he , and he
cha ac e is ic o in e es is a acial demog aphic. No
asso a i e mixing implies no ela ionship be ween he ace
g oups o pa ne s o e he whole ne wo k, while posi i e
(nega i e) associa i e mixing implies ha wo pa ne s a e
mo e (less) likely o belong o he same ace g oup. In he
con ex o his s udy, we a e in e es ed in a pa icula ype o
asso a i i y, one whe e he cha ac e is ic o in e es is he
deg ee o he node. Thus, we a e in e es ed in whe he nodes
wi h high deg ee end o be connec ed o o he nodes o high
deg ee, o no . Wi hin co po a e di ec o ship ne wo ks, he
asso a i i y coe icien is pa icula ly impo an because i
indica es whe he “high- lying” di ec o s end o si on
boa ds wi h o he “high- lying” di ec o s mo e han would
be expec ed unde a andom model.
Small wo lds and andom ne wo ks
The “small-wo ld” phenomenon is he name gi en o he
disco e y o a su p isingly sho chain o in e media ies ha
connec s wo people who had p e iously ne e me . A
classic demons a ion o he small-wo ld e ec was
pe o med by Milg am (1967), who ga e subjec s a le e
oge he wi h an ins uc ion o send he le e o a andomly-
selec ed a ge indi idual – wi h he es ic ion ha hey
could only send he le e on o someone who hey knew on
a i s name basis, who would ecei e simila ins uc ions.
Famously, he le e s ha did ind hei way o he a ge did
so in an a e age o less han six s eps.
In ne wo k e ms, he small-wo ld e ec has been de ined as
a combina ion o a sho a e age dis ance and a high deg ee
o clus e ing. Following his o mula ion, many ypes o
ne wo ks ha e been disco e ed o possess small-wo ld
cha ac e is ics. Howe e , he de ini ion o a small-wo ld
18 S.A .J.Bus.Manage.2009,40(2)
demands ha one p o ide some kind o basis o compa ison
i.e. some way o answe ing he ques ion: “small ela i e o
wha ?” One app oach (e.g. Da is e al., 2003) is o compa e
he ne wo k o a comple ely andom g aph whe e all ha is
known is he numbe o di ec o nodes N, he numbe o
i m nodes M, and he o al numbe o edges in he g aph.
These a e known as Poisson andom g aphs. A di e en
app oach (e.g. Conyon & Muldoon, 2006) is o compa e he
ne wo k o one which has p ecisely he same dis ibu ion o
di ec o ships held and boa d sizes as in he obse ed
ne wo k bu in which connec ions be ween di ec o nodes
and i m nodes occu a andom. These ne wo ks a e known
as andom g aphs wi h a bi a y deg ee dis ibu ions.
S anda d o mulae a e a ailable o he expec ed alues o
a ious ne wo k s a is ics unde assump ions o Poisson o
a bi a y andom deg ee dis ibu ions (e.g. see Conyon &
Muldoon, 2006). Wha is no always made explici is ha
bo h hese compa isons p o ide aluable in o ma ion. The
o me shows whe he a ne wo k is a “small-wo ld” in he
con en ional sense o a ne wo k possessing a simila ly sho
a e age dis ance o a Poisson andom g aph while ha ing a
a la ge clus e ing coe icien . The la e shows whe he
he “smallness” o he small-wo ld can be en i ely explained
by he dis ibu ions comp ising he bipa i e g aph o
whe he he e is some addi ional non- andom s uc u e ha
equi es explana ion. We hus show compa a i e s a is ics
om bo h he Poisson andom g aph and he andom g aph
wi h a bi a y deg ee dis ibu ions.
Li e a u e e iew
Resea ch on co po a e ne wo ks ends o all in o wo b oad
ca ego ies. The olde and mo e well-es ablished o he wo
examines he causes and consequences o in e locks
be ween i ms, iewing he i m as he uni o analysis. This
kind o analysis has he ad an age ha i is no necessa y o
econs uc he comple e i m ne wo k. I is su icien o
iden i y a i m ha sha es a common di ec o wi h ano he
and is hus in e locked, and in es iga e whe he he e a e
any signi ican an eceden s and consequences o his ie.
This is o en known as ‘in e lock’ esea ch, a label we adop
he e. The second ype o co po a e ne wo k esea ch iews
he comple e in e locked ne wo k o i ms (o di ec o s) as
he ocus o analysis. Much o his wo k has conside ed he
s a is ical p ope ies o hese comple e ne wo ks, al hough o
cou se gi en he da a i is also possible o conduc some
i m- o indus y-le el analyses, o example iden i ying
i ms ha ha e he highes deg ee o e alua ing he
asso a i i y be ween indus ies. While many o he pape s
published in his ela i ely new a ea a e conce ned wi h
whe he a ne wo k is a ‘small wo ld’ o no , his is only one
o he opics ha can be add essed. We hus p e e o label
his pa icula di ec ion esea ch in o ‘co po a e sys ems’, i s
de ining ea u e being he conside a ion o he ne wo k as a
whole.
In e lock esea ch
In e lock esea ch is ocused on wha , i any hing, causes
i ms o in e lock, and wha e ec s in e locking di ec o a es
ha e o he i ms in ol ed. Bo h hese in es iga ions ha e a
s ong beha iou al componen .
Causes o in e locks
Hypo hesised causes o in e locks include a emp s a
collusion, coop ing sou ces o en i onmen al unce ain y,
moni o ing, enhancing epu a ion and legi imacy, he ca ee
ad ancemen o he di ec o s in ol ed, and social ies
among he eli e class (Miz uchi, 1996). While collusion ia
in e locks be ween i ms in he same indus y is e ec i ely
p ohibi ed by compe i ion laws, an ea ly s udy ound almos
no associa ion be ween p o i abili y and in e locks wi h
compe i o s in any case (Pennings, 1980). Mo eo e , he e is
no eal eason o sugges ha in e locks a e he mos
e ec i e means o achie e collusion, gi en he possibili y o
de ec ion. The e is mo e e idence o sugges coop a ion as a
possible sou ce o in e locks (e.g. Thompson & McEwen,
1959; Bu 1983), bu he e oo he e a e con lic ing iews.
Mos ies b oken by he dea h o e i emen o he
in e locking di ec o a e no e-es ablished (O ns ein, 1980;
Palme , 1983), sugges ing coop a ion was no a decisi e
ac o in es ablishing he o iginal ela ionship (Miz uchi,
1996). Se e al indings in a ou o a moni o ing
explana ion ha e been made, in pa icula hose inding an
inc eased likelihood o unp o i able i ms o ming in e locks
(e.g. Dooley, 1969; Miz uchi & S ea ns, 1988), especially
wi h banks (Richa dson, 1987; Miz uchi & S ea ns, 1988).
As poin ed ou by Miz uchi (1996), coop a ion and
moni o ing bo h esul om esou ce dependencies and a e
hus di icul o sepa a e empi ically.
The o he explana ions s a ed abo e ocus on he
cha ac e is ics o he di ec o s o ming in e locks a he han
he i ms hemsel es. Di ec o s signal he epu a ion o he
i m on whose boa d hey si (e.g. Selznick, 1984), and
indi iduals a e hus o en chosen on he basis o hei own
epu a ion (Mace, 1971; Useem, 1984). As a consequence,
di ec o s a e mo e likely o be nomina ed o new boa ds i
hey a e al eady a membe o se e al boa ds (Da is, 1993).
O cou se, bo h legi imacy and epu a ion explana ions
equi e ha he po en ial di ec o s be known in he i s
place, and his is a mo e likely o occu wi h a gi en
(uppe ) social s a um. This ea u e has been no ed by
se e al esea che s (e.g. Zei lin, 1974; Useem, 1984) as
e ec i e ‘elemen s o capi al class in eg a ion’ (Miz uchi,
1996).
In summa y, wi h he excep ion o collusion, he e exis s
some e idence in a ou o all o he hypo hesised causes
o in e locks o o m, bu his e idence ends o a y om
s udy o s udy. A sensible app aisal o his body o
knowledge migh he e o e be ha he abo e ac o s a e by
no means mu ually exclusi e, and ha any o hem can
in luence a decision o in e lock a one ime o ano he ,
ei he indi idually o in combina ion wi h one ano he .

S.A .J.Bus.Manage.2009,40(2) 19
Consequences o in e locks
Resea ch in o he e ec s o in e locks on i m beha iou has
yielded nume ous and a ied esul s. Miz uchi (1996) gi es
a summa y o hese, while Da is e al., (2003) and Di Pie a
e al. (2008) p esen he mo e ecen e idence. In e locking
di ec o a es ha e been shown o acili a e he adop ion o
execu i e compensa ion p ac ices such as “golden
pa achu es” (Coch an, Wood & Jones, 1985), “g eenmail”
(Kosnik, 1987), and “poison pills” (Da is, 1991; Da is &
G e e, 1997). O he s ha e ound ha he amoun o ex e nal
inancing a i m ecei es is ela ed o bank ep esen a ion on
i s boa d (Miz uchi & S ea ns, 1994), and ha a ela ionship
be ween in e locks and con ibu ions o poli ical candida es
as well as cong essional es imony exis s (Miz uchi, 1992).
In e locks also se e o acili a e swi ching beha iou
be ween s ock exchanges: Nasdaq-lis ed i ms we e mo e
likely o swi ch o he New Yo k S ock Exchange i he
i ms wi h whom hey we e in e locked had p e iously done
so (Rao, Da is & Wa d, 2000). As Da is e al. (2003) pu i ,
“boa d in e locks may be a o ui ous by-p oduc o boa d
p e e ences o ec ui ing expe ienced di ec o s, wi h li le
s a egic in en … ye he esul is he c ea ion o a ne wo k
ha is highly consequen ial o boa d decision-making”.
In e locks also ha e an e ec on he di ec o s in ol ed in
hem. In e locked di ec o s end o be less e ec i e a
moni o ing (Fich & Shi dasani, 2006) and mo e likely o be
absen om boa d mee ings (Ji apo n, 2007). Mo eo e ,
in e locks also seemingly exe some in luence o e
in es o s: Di Pie a e al. (2008) ind ha in I aly, he
numbe o addi ional di ec o ships held by a boa d o
di ec o s (exp essed as a p opo ion o boa d size) has a
posi i e associa ion wi h he ma ke alue o a i m.
Resea ch in o co po a e sys ems
Following Wa s and S oga z’s (1998) wo k on ‘small
wo ld’ ne wo ks (see Wa s (2003) o Ba abasi (2003) o
popula in oduc ions), simila analyses we e soon applied
o di ec o ship ne wo ks, i s as pa o a heo e ical pape
(Newman, S oga z & Wa s, 2001) and la e as se e al ull-
leng h a icles (e.g. Da is e al., 2003; Conyon & Muldoon
2006). The ocus o hese pape s is on quan i ying he
s uc u e o he di ec o ship ne wo k in i s en i e y, in e ms
o he ne wo k s a is ics iden i ied p e iously. Pa icula
a en ion has been paid o clus e ing coe icien s and
geodesic dis ances, which when la ge and small espec i ely
signal ha he ne wo k is a ‘small wo ld’. Table 1
summa ises p e ious esea ch in o he shape o di ec o and
i m ne wo ks in e ms o he h ee key s a is ical p ope ies
discussed ea lie : a e age deg ee, dis ance and clus e ing.
Resul s di e widely o e he s udies. A e age i m deg ee
a ies be ween 1,1 and 23,8; a e age dis ance be ween 1,8
and 5,1; clus e ing coe icien s o he Wa s-S oga z a ie y
be ween 0,22 and 0,71; and clus e ing coe icien s based on
ansi i i y be ween 0,17 and 0,73. Howe e , di ec
compa isons a e complica ed by di e en choices ega ding
sample design and analysis. These can be summa ised as (a)
whe he o use all publicly aded i ms o a subse o hese
i ms, usually con aining he la ges N i ms, (b) whe he o
es ic a en ion o he la ges connec ed componen o no ,
(c) whe he o compa e he empi ical ne wo k o a Poisson
o a bi a y andom g aph. These choices a e o en dic a ed
by he aims o a pa icula piece o esea ch. The s udies ha
mos closely esemble ou own a e hose o Conyon and
Muldoon (2006).
Da a
The ne wo k ha we in es iga e comp ises he boa ds o
di ec o s o all JSE-lis ed Sou h A ican companies as a 1
Ma ch 2008. This in o ma ion was ob ained om he
McG ego BFA da abase and checked manually o
consis ency. One p oblem ha a ises is ha companies may
p o ide di e en le els o de ail in he names o hei
di ec o s, o example in he numbe o ini ials ha a e
speci ied. Ou app oach has been o co ec only ob ious
e o s and omissions ( o example, NJM Canca and NJMG
Canca a e p esumably he same pe son). The esul ing
da ase con ains 2747 di ec o s and 397 i ms.
Resul s
We begin by gi ing a b oad o e iew o he cu en s a e o
co po a e di ec o ship in Sou h A ica, aided by he
desc ip i e s a is ics in Table 2, which a e gi en bo h o he
ull ne wo k and he la ges connec ed componen al hough
in he ollowing we p ima ily epo he esul s om he ull
ne wo k.
The a e age numbe o di ec o s si ing on he boa d o a
JSE-lis ed company is 8,56, anging g ea ly om jus wo
di ec o s o 27. This mean boa d size is be ween he alues
epo ed by Conyon and Muldoon (2006) o he USA (9,97
membe s) and he UK (6,51 membe s) and Ge many (6,33
membe s). The ull dis ibu ion o boa d sizes is shown in
Figu e 4(b), which shows a dis ibu ion ha is somewha bu
no g ea ly skewed o he igh – he coe icien o skewness
is 1,1 bu he median boa d size is eigh , e y close o he
mean. The a e age numbe o di ec o ships held is 1,28, and
he o e whelming majo i y o di ec o s (83%) a e membe s
o jus a single boa d. This a e age numbe o di ec o ships
held in Sou h A ica is ma ginally lowe han hose epo ed
by Conyon and Muldoon o he USA (1,63 di ec o ships),
UK (1,84 membe ships) o Ge many (1,45 membe ships),
bu he p opo ion o single-boa d di ec o s ma ches closely.
This sugges s ha di e ences exis p edominan ly in he
igh - ail, pe haps due o he la ge numbe s o i ms
occupying hose ma ke s. Figu e 4(a) shows he ull
dis ibu ion o di ec o ships held, bu he e equencies a e
shown on a loga i hmic scale because he dis ibu ion is so
igh -skewed ( he coe icien o skewness is 4,1 and he
median is o cou se one). The e a e jus 32 di ec o s (1,2%)
who hold i e o mo e boa d membe ships – in he absence
o loga i hmic scaling, his de ail in he igh - ail is
impossible o dis inguish.
20 S.A .J.Bus.Manage.2009,40(2)
Table 1: Summa y o p e ious esea ch analysing he s a is ical p ope ies o i m and di ec o ne wo ks. The able
shows he a e age deg ee z, a e age geodesic dis ance L, and wo clus e ing measu es ( he ansi i i y-based c and he
Wa s-S oga z clus e ing measu e cWS), o bo h he i m- and di ec o -p ojec ions, whe e a ailable. The inal wo
columns indica e whe he he ull se o publicly-lis ed i ms was used o a subse o ‘la ges ’ i ms, and whe he he
analysis was es ic ed o he la ges componen only
Fi m p ojec ion Di ec o p ojec ion
Coun y Yea Re e ence Fi ms Di s z L C
C
WS z L C
C
WS
Full
ne wo k?
La ges
comp
used?
Denma k 1993 Kogu and Belinky (2008) 313 23,8 2,5 0,73 Unclea No
Denma k 2000 Sinani e al (2008) 155 1129 3,1 5,1 0,51 11,3 5,9 0,93 No Yes
Denma k 2003 Kogu and Belinky (2008) 534 2,7 3,7 0,54 Unclea No
Ge many 1993 Kogu and Belinky (2008) 304 7,5 2,6 0,39 Unclea No
Ge many 2000 Kogu and Belinky (2008) 630 7,8 2,9 0,38 Unclea No
Ge many 2002 Conyon and Muldoon (2006) 582 4185 4,6 2,9 0,41 0,58 14,5 6,4 0,93 0,72 Yes Yes
Ne he lands 1996 Heemske k and Schnyde (2008) 194 1771 8,0 3,0 0,38 12,8 3,8 No Yes
Ne he lands 1997 Kogu and Belinky (2008) 1152 3,8 4,0 0,56 Unclea No
Ne he lands 2001 Heemske k and Schnyde (2008) 137 1721 7,0 3,2 0,35 11,4 3,9 No Yes
Ne he lands 2001 Kogu and Belinky (2008) 2253 2,4 3,3 0,63 Unclea No
No way 1990 Kogu and Belinky (2008) 53 1,4 4,2 0,48 Unclea No
No way 2000 Sinani e al (2008) 23 78 3,5 3,6 0,71 7,7 3,1 0,92 No Yes
No way 2000 Kogu and Belinky (2008) 301 1,1 1,8 0,72 Unclea No
Sweden 1990 Kogu and Belinky (2008) 229 5,0 3,0 0,42 Unclea No
Sweden 2000 Sinani e al (2008) 265 1457 5,3 4,0 0,40 14,6 4,8 0,88 Yes Yes
Sweden 2000 Kogu and Belinky (2008) 352 3,1 3,7 0,43 Unclea No
Swi ze land 1990 Heemske k and Schnyde (2008) 96 888 8,2 2,6 0,40 17,8 3,4 No Yes
Swi ze land 1990 Kogu and Belinky (2008) 96 4,1 2,6 0,41 Unclea No
Swi ze land 2000 Heemske k and Schnyde (2008) 95 848 4,4 3,8 0,42 14,2 4,8 No Yes
Swi ze land 2000 Kogu and Belinky (2008) 238 2,4 4,0 0,52 Unclea No
UK 2002 Conyon and Muldoon (2006) 1732 8850 5,7 4,1 0,38 0,38 9,0 6,5 0,89 0,61 Yes Yes
USA 1982 Da is, Yoo and Bake (2003) 581 5853 10,0 3,4 0,24 19,0 4,3 0,88 No Yes
USA 1990 Da is, Yoo and Bake (2003) 524 4768 8,8 3,5 0,24 17,0 4,3 0,87 No Yes
USA 1999 Newman, S oga z and Wa s (2001) 914 7673 14,4 4,6 0,88 0,59 No No
USA 1999 Da is, Yoo and Bake (2003) 516 4538 8,6 3,5 0,22 16,0 4,3 0,87 No Yes
USA 2003 Conyon and Muldoon (2006) 1473 11057 7,3 3,5 0,23 0,17 13,5 5,2 0,87 0,56 Yes Yes
Table 2: Desc ip i e s a is ics on he p o ile o co po a e di ec o ship in Sou h A ica (all means gi en wi h associa ed
s anda d e o s in pa en heses)
Full ne wo k La ges connec ed componen
Di ec o sea s 3398 2764
Numbe o unique di ec o s 2653 2048
Numbe o i ms 397 294
A e age boa d size 8,56 (0,19) 9,40 (0,22)
Maximum boa d size 27 27
Minimum boa d size 2 4
A e age numbe o di ec o ships 1,28 (0,02) 1,35 (0,02)
Maximum numbe o di ec o ships 9 9
One-boa d di ec o (%) 83% 79%
Two-boa d di ec o (%) 11% 13%
S.A .J.Bus.Manage.2009,40(2) 21
Numbe o di ec o ships held
Numbe o di ec o s
123456789
1
10
100
1000
Numbe o boa d membe s
Numbe o i ms
3 7 11 15 19 23 27
0 20406080
Figu e 4: His og ams showing he dis ibu ion o (a) he numbe o di ec o ships held, and (b) he numbe o membe s
pe boa d. No e ha he o me is measu ed on a loga i hmic scale because i is ex emely igh -skewed.
Ha ing examined hese basic s a is ics, we now u n o a
mo e de ailed analysis o he s uc u e o he co po a e
di ec o ship ne wo k. Table 3 shows he sizes o he wo
la ges componen s in he di ec o - and i m-p ojec ions o
he di ec o ship ne wo k. The deg ee o connec i i y
exhibi ed in bo h he di ec o and i m ne wo ks is ai ly
high – oughly h ee-qua e s o all di ec o s and all i ms
a e connec ed by some pa h. A simila le el o connec i i y
was epo ed by Conyon and Muldoon (2006) o he Uni ed
Kingdom, wi h sligh ly highe connec i i y epo ed o he
USA.
Table 3: Absolu e and ela i e sizes o he wo la ges
componen s in he di ec o - and i m-p ojec ions
La ges connec ed componen – i ms 294 (74%)
2nd la ges connec ed componen - i ms 6 (2%)
La ges connec ed componen - di ec o s 2048 (77%)
2nd la ges connec ed componen - di ec o s 20 (1%)
Table 4 and 5 show he mos impo an o he ne wo k
s a is ics: he a e age deg ee, dis ance, clus e ing
coe icien , and he asso a i i y coe icien , o he ull
ne wo ks and o he la ges connec ed componen
espec i ely. Also p esen ed in hese ables a e alues o
hese quan i ies ha would be expec ed unde di e en ypes
o andom ne wo k models. The wo ne wo k models used
a e hose discussed ea lie in he sec ion “Small wo lds and
andom ne wo ks”. The Poisson andom g aph esul s show
wha quan i ies would be expec ed i only he o al numbe
o connec ions was cons ained, bu he dis ibu ion o
connec ions as well as how hose connec ions a e o med
we e allowed o be andom. These esul s a e la gely o
in e es because hey allow one o in e whe he a ne wo k is
a “small-wo ld” o no – he con en ional de ini ion o a
small-wo ld ne wo k being one ha has a simila a e age
dis ance o a Poisson andom g aph while ha ing a much
la ge clus e ing coe icien . The andom g aph wi h
a bi a y deg ee dis ibu ion shows wha would be expec ed
i he en i e dis ibu ion o di ec o ships and boa ds we e
ixed (i.e. a hose shown in Figu e 4(a) and (b)) and only
he connec ion o i ms o di ec o s was a andom. These
expec ed alues can be used o in e whe he he e is any
addi ional s uc u e ha is no accoun ed o by a “small-
wo ld” ne wo k model.
The a e age di ec o in Sou h A ica sha es a boa d wi h
jus o e 11 o he di ec o s. Tha is, hey a e in di ec
con ac wi h some 11 people. I a en ion is es ic ed o he
la ges connec ed componen , his igu e ises o almos 13.
This inc ease occu s because he i ms ou side he la ges
componen ha e on a e age bo h smalle boa ds (Mann-
Whi ney Z = 8,4, p < 0,001) and ewe in e locks wi h o he
companies (Mann-Whi ney Z = 14,1, p < 0,001). The
a e age dis ance be ween wo di ec o s in he ne wo k is jus
4,3. The smallness o his igu e is no less ema kable o
he ac ha i has been obse ed in so many ne wo ks: in a
ne wo k o o e 2500 di ec o s, wo di ec o s can be
connec ed using a pa h consis ing o jus h ee in e media e
di ec o s. The ne wo k is also highly clus e ed ela i e o
wha would expec om a pu ely andom Poisson g aph.
The high deg ee o clus e ing ela i e o a Poisson andom
g aph oge he wi h his sho a e age dis ance is a hallma k
o he “small-wo ld” ne wo k. I is he e o e clea ha he
ne wo k o co po a e di ec o s in Sou h A ica can be
desc ibed as a small wo ld.
22 S.A .J.Bus.Manage.2009,40(2)
Table 4: Ne wo k s a is ics o he di ec o - and i m-p ojec ions, wi h s a is ics ha would be expec ed om andom
g aphs wi h he same dis ibu ions o di ec o ships and boa d sizes bu andom connec ions (A bDD), and om
comple ely andom g aphs (Poisson). All obse ed means gi en wi h associa ed s anda d e o s.
DIRECTORS FIRMS
Obse ed A bDD Poisson Obse ed A bDD Poisson
Deg ee 11,397 0,181 11,737 11,397
5,234

0,293 6,470 5,234
Dis ance 4,3120,024 3,801 3,240 3,654

0,061 3,127 3,615
Clus e ing ( ans.) 0,5730,006 0,593 0,004 0,293

0,008 0,248 0,013
Clus e ing (W-S) 0,9160,004 – – 0,266

0,016 – –
Asso a i i y 0,256 0,008 0,115 0
0,245

0,029 0,131 0
Table 5: Ne wo k s a is ics o he la ges connec ed componen s o he di ec o - and i m-p ojec ions, wi h s a is ics
ha would be expec ed om andom g aphs wi h he same dis ibu ions o di ec o ships and boa d sizes bu andom
connec ions (A bDD), and om comple ely andom g aphs (Poisson). All obse ed means gi en wi h associa ed
s anda d e o s.
DIRECTORS FIRMS
Obse ed A bDD Poisson Obse ed A bDD Poisson
Deg ee 12,923 0,220 13,342 12,923 6,918

0,344 8,501 6,918
Dis ance 4,3120,024 3,298 2,980 3,654

0,061 2,618 3,942
Clus e ing ( ans.) 0,555 0,006 0,544 0,006
0,291

0,009 0,207 0,024
Clus e ing (W-S) 0,896 0,005 – –
0,332

0,018 – –
Asso a i i y 0,195 0,008 0,088 0
0,219

0,028 0,105 0
A social ne wo k will, excep in pa hological cases, exhibi
small-wo ld cha ac e is ics as a esul o i s s uc u e i.e.
indi iduals belong o g oups, so ha non- i ial clus e ing is
almos always p esen , and g oup sizes di e , inducing
co ela ions be ween he deg ees o adjacen nodes
(Newman & Pa k, 2003). Thus he iden i ica ion o a
co po a e di ec o ship ne wo k as a small-wo ld is on one
hand in e es ing and on he o he en i ely expec ed. This is
e lec ed in he s ong ag eemen be ween he obse ed
alues and he expec ed alues o a andom g aph wi h
a bi a y deg ee dis ibu ions, o he a e age deg ee and
clus e ing. The simila i y exis s o a lesse ex en o he
a e age dis ance, al hough e en he e he igu es emain in
ough ag eemen . All hese indings a e in subs an i e
ag eemen wi h hose epo ed by Conyon and Muldoon
(2006) and Sinani e al. (2008). In hose s udies, a e age
deg ees a ied be ween 9,0 o he UK and 14,6 o Sweden;
dis ances anged om 4,8 in Sweden o 6,5 in he UK; and
( ansi i i y-based) clus e ing coe icien s di e ed om 0,56
in he USA o 0,72 in Ge many. The alues we obse e in
Sou h A ica a e simila , and he deg ee and clus e ing
s a is ics ( ega dless o whe he he ansi i i y-based o
Wa s-S oga z clus e ing is used) all wi hin hese in e als.
The a e age dis ance is sligh ly lowe han ha epo ed by
Conyon and Muldoon (2006), bu his may a leas in pa be
due o he smalle ne wo k s udied he e. Fu he mo e, he
closeness o ma ch be ween obse ed and expec ed deg ees
and clus e ing, as well as he sligh ly longe - han-expec ed
a e age dis ance, we e also all epo ed by Conyon and
Muldoon (2006). Sinani e al. (2008) use he Poisson
andom model as a basis o compa ison, and hus
di e ences be ween hei expec ed and ac ual esul s a e no
di ec ly compa able wi h ou s.
Thus he Sou h A ican co po a e landscape is a small-
wo ld, and is o a simila s uc u e o he p e iously s udied
coun ies, in pa icula he USA and UK. Wha is a less
ob ious is whe he he e is any addi ional s uc u e beyond
he small-wo ld ha emains. In espec o his, he
asso a i i y coe icien plays a key ole. As men ioned,
posi i e asso a i i y is o be expec ed in mos social
ne wo ks, and gi en he pa icula dis ibu ions o boa d
sizes and di ec o ships in Sou h A ica, he expec ed
asso a i i y is 0,12. This makes he obse ed asso a i i y
coe icien o 0,26 in Table 3 o special in e es . The
p esence o ypical social ne wo k s uc u es (essen ially,
g oups o di e en sizes) is only su icien o explain abou
40% o he co ela ion ha is obse ed. Newman and Pa k
(2003) ind almos p ecisely he same esul s (an
asso a i i y coe icien o 0,28 agains an expec ed alue o
0,12) o i ms in he USA. Conyon and Muldoon (2006)
also ind posi i e asso a i i y, bu do no compa e i o any
benchma k. I is hus di icul o d aw a compa ison wi h
hei s udy, bu i is ai ly clea ha he e is addi ional
s uc u e in co po a e di ec o ship ne wo ks, and ha his
e ec is p esen in Sou h A ica oo. No e ha he absolu e
asso a i i y is lowe in he la ges connec ed componen
because mos di ec o s ou side he main componen will
end o ha e ela i ely ew connec ions, and will hus end o
be connec ed o o he di ec o s o simila ly low deg ee.
Ne e heless, he same subs an i e inding – ha his
asso a i i y is well beyond wha one would expec om a
andom g aph – s ill holds. One in ui i ely a ac i e
explana ion ha has been pu o wa d by Newman, S oga z
and Wa s (2001) is ha di ec o s who si on many boa ds
end o si on hose boa ds wi h di ec o s who hemsel es si
on many boa ds. This e ec has been called he “homophily