An analysis of corporate board networks in South Africa

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