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Page 1: Network theory

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On Network Theory� Network Theorizing ��������( � �� �� �� � ) � � � � � � � � � � � � � � � �

� ��������������������

� �� � ���� � ���� � ���� � ��

� Characterizing Network Theory � ��� � � ��� � � ��� � � ��� �

� �� �� �� � ( � �� �� �� � )� � � �� � �� � �� � � (Flow Model)

� � � � �� � � � �� � � � �� � � � ��(Bond Model)

� � � � � �� � � � �� � � � �� � � � � (Mathematical Object )

�� � � � � � (Network Theory)

�������(Theory of Networks)

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������� � � � (Network Theory ) � �� �������������������� Granovetter’s (1973) strength of weak ties

(SWT) theory� �� � ���� � ���� � ���� � �� Burt’s (1992) structural holes (SH) theory.

Network Theorizing ������������������������

Mark Granovetter

Joan Butler Ford Professor in the School of Humanities and Sciences, Department of Sociology, Stanford University.

Ph.D. Sociology, 1970, Harvard University

A.B. American and Modern European History, 1965, Princeton University

Ronald S. Burt

Hobart W. Williams Professor of Sociology and Strategy, University of Chicago Booth School of Business

PhD in sociology from the University of Chicago in 1977

bachelor's degree in social and behavioral science, 1971, Johns Hopkins University

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�������������������� SWT theory � � � � � � �

� ��������1����� � � � � � �� � � � � � �� � � � � � �� � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �

� A�B � � � � � (strong tie )�B�C� � � � � � (strong tie )��A�C� � � � � � � � � � �� � (weak tie) (A�C � � ! �" # $ % &�' )

� () A�C*+ � , &� - � �� � �� &. / 0 1 g-transitivity (Freeman 1979). ( 2 3 / 4 2 )(g for Granovetter )

� *+ 2 3 / 4 2 (transitivity)&� - � �� � �Granovetter 5 1 6 7 8 9 (: ; (homophilous )&! : < = > � ( ? @ " A &�1 � � )

� B C *+ 9 (: ; &> � �D E FG 8 H I 4 2 (weakly transitive ) =>A�B( J K �L M &H I ) " : N �B�C ( J K �L M &H I ) " : N �O PA�C ( J K �L M &H I ) � E " : N

���������2����� �� �� �� � � � � � � � � � � � � � ! " # � $ % & '� � � � ! " # � $ % & '� � � � ! " # � $ % & '� � � � ! " # � $ % & ' (bridging ties are a potential source of novel ideas)

� Q R - S(bridging ties)T�7 U � V W &X ! � � �

Network Theorizing ������������������������

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� � � � ��� � �Granovetter � � � � � ! " # $ % &' ( ) ( � �� �� �� �)�� * + , -( ) ( ) ( ) ( ) ����� � * � � � � � � * � � � � � � * � � � � � � * � � � �

� Y Z [ \ ] ^ _ [ ` Ta b A�Gc - S(strong tie )�O P K @ d G�A&� � � �e f � � ^ g � � � �� � (weak tie)hO P A�G � � &-Si FE � j ` k l m H I &Q R - S( n � ` k o p &H I / I q )

( � ( � ( � ( � ����+ , � � � - . � � � & '+ , � � � - . � � � & '+ , � � � - . � � � & '+ , � � � - . � � � & ' � / � 0 � 1 2 � 3 4 � 5� / � 0 � 1 2 � 3 4 � 5� / � 0 � 1 2 � 3 4 � 5� / � 0 � 1 2 � 3 4 � 5

� n � r s t V W &u - S�v � � � �1 ` k V W &w x H I

Network Theorizing ������������������������

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. / � � 0 1 2 3 Granovetter�������������������� SWT theory�4� 5 6 -

� � � � � � �� � � � �� � � � �� � � � �� �

� Mark S. Granovetter’s(1973) y z { Newton | } 282 ~ � � / , � � � � �� � � � L � � &� � � 6 �� � � / � � & � � � &! � L � � � �^ � 5 � &! � ) � � L �� e � � �   ! ¡� � / ¢ n � 17% �£ ¤ &� � � � ) � ¥ � � &¦ E ¡

� � � � � � (individual social capital )-� � § ¨ u - S&~ © �ª « y $ E § 1 �¬

� ! " # $ % (group)�& ' �( ) * -� # ­ � l &$ ® �� ¯ , ° ± ² ³ � ´ � &$ < / % ©� µ ¶ � &u - S· �% © ¸ ¹ &$ E H º �� F# % © » ¼ ½ � ¾ �¿# À Á

Network Theorizing ������������������������

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�� ��� ��� ��� � Burt SH theory � + , - . / 0� � 12� A % 6 7 8 9 � 9 : ; ! < =% 6 7 8 9 � 9 : ; ! < =% 6 7 8 9 � 9 : ; ! < =% 6 7 8 9 � 9 : ; ! < = > ?> ?> ?> ? A � @ A ? B� @ A ? B� @ A ? B� @ A ? B BC D � - . � �C D � - . � �C D � - . � �C D � - . � �

� A�B ^ à � Ä ~ - S( Å Æ - Sc Ç " # )� B�X�YL M &H I � � o p &� A&H I � 6 � � Ä ~ F# &< µ �È L A, É F# / w x H I &Ê Ë Ì

Network Theorizing ������������������������

���������� � � � � � �� � � �

�� � � � � � � �� �� � ! " # $ % & '

( ) * (+ , " �A- � a.B- " � b/ 0 1 2 3 4 !" # $ 5 6 ( ) * � � � �)7

Burt 8 9 � ! " � : ; < � � � = > ? 9 @ A �� ! " � : ; B C % ' D � E F GE H I J K 7L M

N O � � = > �P Q R �( ) * �� � S T U ��

�' � � �V W � � � �X U E F .Y Z [ \

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������������ SWT theory������ ��� ��� ��� � Burt SH theory��� � � ���� � � ���� � � ���� � � �

� � E F G H I J K� E F G H I J K� E F G H I J K� E F G H I J K

� AL M ÌBÎ ¨ �o p &� ÏH I �(Burt’s S· Ð ��C Ñ �A� § ¨&S· Ð ( ¢ Ò � § Í)�ÏGranovetter’s u - S��C Ñ �A� § ¨ &-S(Bridges)

� F�0 Ó *+ � � 1 �o p � &- S(tie) � R Ô (bridge)�Sb  AÌBL M Î ¨ � Ï&w x H I

� Granovetter� Õ Ö × (DV)TL M � �� 7 Ö × (IV)TÎ ¨ �o p � &H I

� Burt� Õ Ö × (DV)TL M Ø Ù� 7 Ö × (IV)TÎ ¨ �o p � &H I

� Ú ~ ��} 8 ��a Û Ü Ý � Ï�Þ 8 # à &ß ¸ à á (based on the same underlying model)

Network Theorizing ������������������������

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������������ SWT theory������ ��� ��� ��� � Burt SH theory��� � � ���� � � ���� � � ���� � � �

� L M � N O % ,L M � N O % ,L M � N O % ,L M � N O % , T

� Granovetter���� � - S�H I � â &ã B � � ä �Burt ��å æ �K ç è é � ä (Kilduff ,2010 )

� Granovetter 5 1 u - Sv � ��� Ï&H I R Ô hBurt�F5 # ê ^ ë ì�� e ` k í î î Z �ï m *g u - SR Ô ð � � E 7 B ñ ò ó ô

(decay) hBurt&Ð ë y 8 ä õ - Sc Ç &ö ÷ �H I � 6 &�o p �(non-redundancy) v � ø ù

� Granovetter � J ��” � Ï” - S(strength of ties)&ú û üdistal causeýhBurt�� J þ �� ø - S(bridging ties)&� û (proximal cause)

� [ / L M ^ ~ � ! � � � � �F � �& � � � h / � , � M r û

�` k ��Î c &Þ � ü“captures the causal agent directly and thus provides a stronger foundation for theory” (Burt 1992, p. 28).ý

Network Theorizing ������������������������

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3 4 � � 5 6 �7 8 (meta-theoretical point of view)0�9 � : ; < =1 SWT�12 > SH� � ? � @ A B

�12 (structure )�C D (position )�E F G H � � I J K L M �7 N� �������������������������������� � � �� � � � �� � � �� � � � �� � � �� � � � �� � � �� � � � �� � � � � � � ��� � � � � � ��� � � � � � ��� � � � � � ��

� � � � ��� � � �� � � � ��� � � �� � � � ��� � � �� � � � ��� � � � (cluster) � � � �� � � �� � � �� � � � � ! " # � $� ! " # � $� ! " # � $� ! " # � $

� � �% & �� ' � (� �% & �� ' � (� �% & �� ' � (� �% & �� ' � ( � ) * + � �, - �� �. / 0 �% 1 2 3� ) * + � �, - �� �. / 0 �% 1 2 3� ) * + � �, - �� �. / 0 �% 1 2 3� ) * + � �, - �� �. / 0 �% 1 2 3

4 � 5 6 7 8 9 � : ;4 � 5 6 7 8 9 � : ;4 � 5 6 7 8 9 � : ;4 � 5 6 7 8 9 � : ;

� ] ^ % ' _ � D ` I a b (c P de f K Gg h I J : )� N i j M D � D ` k l m n : �N 1 o p + �q N @ A �r 1 M & s t u

v w @ �x y ! ( ) I 2 z { � | }

� M & u v ~ � � � & � � �w @ �N � ( ) � � P � z { � �

� ³ ¹ i () Ú ~ �� � � C Ñ � 7 8 � P � % , � � � Q R S T U7 8 � P � % , � � � Q R S T U7 8 � P � % , � � � Q R S T U7 8 � P � % , � � � Q R S T U

� < = , - > ? @ A 6 7 8 B � C -< = , - > ? @ A 6 7 8 B � C -< = , - > ? @ A 6 7 8 B � C -< = , - > ? @ A 6 7 8 B � C -

� D � � E 8D � � E 8D � � E 8D � � E 8 (flow) F C -F C -F C -F C - (pipe) � G H ' I� G H ' I� G H ' I� G H ' I

� � ' � � � U & � � � � � d! � � � �E F � � � �� �

� � ' � � �� p � � � � � � � SWT.SHs t � �   ¡ ¢ 7c P �£ ¤ ¥U 2 ¦ § q ��̈ E F © < �ª "   : ; � § q « 7

� E F © � � ( Q ¬­ ® � �G�̈ ­ � ¯ @ ° E F © ± ²� p ³ ´ � 9 &

� z � (µ P e f K G¶ · ¸ ¹ º � � � b G» ­ ¼ ½ ¾ ¾ )

Characterizing Network Theory ��������������������������������

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Flow & Pipe modelO P V W � ) X Y � Z [ ! 9 � \ ]V W � ) X Y � Z [ ! 9 � \ ]V W � ) X Y � Z [ ! 9 � \ ]V W � ) X Y � Z [ ! 9 � \ ] ̂ _ � ` ? a C D L M b c^ _ � ` ? a C D L M b c^ _ � ` ? a C D L M b c^ _ � ` ? a C D L M b c

� J K � � � 8 B L MJ K � � � 8 B L MJ K � � � 8 B L MJ K � � � 8 B L M

� � � y F# ! � � � � � � } FE # � � � y Ú ~ ! � ) h

� � � � H I & � � ��A4 2 M B& � � �AE � ! º� J K � � � - N F O PJ K � � � - N F O PJ K � � � - N F O PJ K � � � - N F O P

� " a � � FE o # $ % # ^ ! �û 1 *~ & ' ( ) � * +

� " } &� � Ñ , - �E ¨ ¹ . 4 M # ^ ! / ¨ �û 1 4 2 &! Fë L¥ � 0 & ' ¥ 1 ê ^ H I h

� � 2 � � ( 3 4 *g � Ñ , - FE y # ^ � 5 ( � �) ) o # Tû 1 AFE 6 " # � � / � Ñ 7 Bï ] 8 ¹ ( Å Æ A9 : ; & < )

� (��S· &) Q R �S T UQ R �S T UQ R �S T UQ R �S T U

� ð = é , É > ¹ H I &M ¾ � � (" �§ q � � �¿ < 2 ¦ § q À )� ð = é , É H I ? @ A B ¾ M ^ 4 C

� C () *g D � Sb �� (y à E ¢ F 3 4 �F# 8 í î � � G ¢ H? &Sb hB C à E &½ I Sb J K # 8 í î ¢ H ? & D � · L

� the likelihood of getting a job (Granovetter 1973, 1974), � being promoted (Brass 1984, 1985; Burt 1992), � being creative (Burt 2004, Perry-Smith 2006).

Characterizing Network Theory ��������������������������������

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Flow & Pipe model � � � �� � � �� � � �� � � �

� ê ^ à E � « È Ï&� M ��& N O � � P F Q ^ &^ ~ h * V W X �* V W X �* V W X �* V W X �

Y Z 0 [ � ��\ ] ^ � � * G HY Z 0 [ � ��\ ] ^ � � * G HY Z 0 [ � ��\ ] ^ � � * G HY Z 0 [ � ��\ ] ^ � � * G H

� ����____` a , - ��� b c d e f g` a , - ��� b c d e f g` a , - ��� b c d e f g` a , - ��� b c d e f g (the exercise of power in exchange networks,Cook and Emerson,1978 )

� í R S T U � = é ) & V ~ W �/ X �³ � ! Y Z t [

� = é B& \ ] � 7 8 ^ _ � =>³ � = é ` a � B� b & = é D   � c� � � 1T�³ P d � - S& = é Y Z - S�K @ d Î Í&¢ Ò e f� � � 2T \ ] " } � T g c �u � g u �c h

Characterizing Network Theory ��������������������������������

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Flow & Pipe model � � � �� � � �� � � �� � � �

� h ���&� i » j ¼ ? (power)& k " l m � flow model& n o �� ¼ ? 6 7 8 ð = é y ��¢ &S· e f ( C �H I �H 6 & � � )� þ � p q &F ¼ ? & � � �C ´ � = é � &" } c u � �

� r ^ + ä s ��� i » j ¼ ? (Network Power)& t Ç » u (coordination )� v w � x (virtual amalgamation )

� Principle behind UnionizationTF y z E Î � ¼ ?

Characterizing Network Theory ��������������������������������

E Á Â Ã A1-A4 Ä Å Æ Ç

A1-A4 È M �T U É ( �EÊ + Ë / Ì Í Î Ä Å K ±A1-A4 È M É ( � � & ' Ï Ð � ÑÒ _ �ÓEÔ � N Ì Í Î Ä Å K ±

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� � � � (coordination )�� ! "�� ! "�� ! "�� ! " (virtual amalgamation ) # $ # $ # $ # $

� ? Q R S T - � � " # (network organization, Jones et al. 1997, Powell 1990 )

� { z ~ © µ ¶ | ê } £ » u ���Î � ¼ ? & ~ ^ ~ © ( % � )

� � / 6 ê ^ � � ä � U V �� (virtual capitalization )� = é � &- S� � © &� � � � � � (capabilities) � 3 � � ~ ^ ~ © �� � í � ) � 9 � ê ^ � 3 � � � ( � E � � )

� # Ã & ; W ( X Y Z /[ � � � (principal/agent theory)\ ] ^� � �! Þ 8 � � ! &G � � Z � � ( � � ! � X � 7 � )

� � � = 1(tie)_ ` a b �c a d e ( � y ^ � )�f 1(bond)� � / � < Sé a # ~ ^ ~ © ^ � Z �

� � � Î � � ¼ (capabilities)

� Bond or Coordination model

Characterizing Network Theory ��������������������������������

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Bond or Coordination modelO P V W � ) X Y � Z [ ! 9 � \ ]V W � ) X Y � Z [ ! 9 � \ ]V W � ) X Y � Z [ ! 9 � \ ]V W � ) X Y � Z [ ! 9 � \ ] ̂ _ � ` ? a C D L M b c^ _ � ` ? a C D L M b c^ _ � ` ? a C D L M b c^ _ � ` ? a C D L M b c

� g h i �j k l m �9 n o p q �r s K t u �v <

� A=E<C<B=C

� g h i �t u v < 9 � w s - xg h i �� y z 8 ? {

� | u � � t u �} ~ graphtheoretic power index (Markovsky et al. 1988) and beta centrality (Bonacich 1987, 2007)

� ` � 12 C D (isomorphic )�g h �� � � j * �� �� AxH� � 12 C D j ` �� ? j ) * � �

Characterizing Network Theory ��������������������������������

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Mathematical Object� � � � � � � � � R �2 F �( 9 � O P � R � � � �: � � � �

� � 8 �� � /� � o (transitivity )� � � � � � � z � y �5 � � % �� � � � =>� � � � � � � �   ¡ ¢ �� £ ¤ (Rapoport, 1963)

� ê ^ � � � SWT&SH��&Þ �� 9 � � � R � ¥ � � ¦ § ¥ �� �

� " a � � ¢ � � � Á (betweenness centrality)� Ú ~ �´ � = é & � � � ` � _ - S*Ú ~ = é � 5 &] Ä / ¡*~ ] Ä / � ( � � Ú / & � � h � ^ ~ é e � 2 ¨ &- S³ � = é &�   (geodesic)� 5 ��ê é � � l & � � � ¢ (betweenness centrality)¡

Characterizing Network Theory ��������������������������������

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Mathematical Object��F ~ n ~ $ E . &· L �� � ( a � × . � �ì �Ü ¡ w ��

� � Q ¨ © ª « x¬ F X : � � � �­ � ® � � 7 N � � (Social Role Theory, Linton (1936), Nadel (1957), Merton (1959), and others) ¯ § ¥

� structural equivalence (Lorrain and White 1971) � regular equivalence (Everett and Borgatti 1994, White and Reitz 1983)

� � � 5 6 : � � � Q ° ± ² ¥ �¬ F � 0³ � � _ ´ µ 12 " �

� clique (Luce and Perry 1949), � n-clique (Luce 1950)� k-plex (Seidman and Foster 1978)

� & ' Õ Ö Cliques × � 1 & ' Ø Ù _ ¦ � Ú ' § q È M 1 < ! " 2 ¦ qW � Û Ü É ( � 7Ý ` � Õ Ö C Þ 1 ß �& ' à ( ) " Ú & ' § q È M �

�á â ã É ( 7� ä å æ ç & q � C Þ Ó� p �Õ Ö " è é & � N 1 ¯ ê

Û Ü É ( � q 7 (n-cliques, n-clans, and k-plexes)

Characterizing Network Theory ��������������������������������