Lse 2003 Complexity Connectivity

TOWARDS AN ORG. CONNECTIVITY FRAMEWORK TOWARDS AN ORGANISATIONAL CONNECTIVITY FRAMEWORK

Eduardo Castellano LSE Complexity Research Programme Workshop 15th July, 2003 London School of Economics (UK)

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK

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Levels of Connectivity 1. Degree of connectivity – The NK model 2. Complex networks pattern of connectivity – Small World model 3. Quality of connections – SN theory 4. Future Research Lines

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK

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Levels of Connectivity 1. Degree of connectivity – The NK model 2. Complex networks pattern of connectivity – Small World model 3. Quality of connections – SN theory 4. Future Research Lines

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (1/11) Description Model conceived by Stuart A. Kauffman (Origins of Order, 1989): It’s a tunable model of fitness landscapes, based on random boolean networks, designed to capture the statistical structure of the rugged multipeaked fitness landscapes seen in nature In the NK model: N represents the number of parts in a system (genes in a genotype...). Each part makes a fitness contribution which depends upon that part and upon de K other parts among the N; therefore K represents the number of linkages, connectivity, each gene has to other genes in the same genotype If the fitness contribution of each gene is affected by a large number of other genes (K high), the possible conflicting constraints are both unknown and likely to be extremely complex. The NK model attempts to capture the the statistical features of such highly interactive epistatic webs with a random fitness function Fitness contributions are drawn from a uniform distribution ranging from 0.0 to 1.0 Each genotype has a “fitness” and the distribution of fitness values over the space of genotypes constitutes a “fitness landscape”

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (2/11) Example (for N=5, K=2)

(*) table extracted from Mitchell A. Potter, http://cs.gmu.edu/~mpotter/nk-generator/ E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (3/11) Properties and insights from the NK model - Landscape Ruggedness and the Complexity Catastrophe: As K increases, the number of peaks in the fitness landscape increases and the landscape becomes more rugged (low correlation between the fitness and similarity of genotypes) K=0

produces a smooth highly correlated landscape with a single peak – ORDER

K=N-1

produces a landscape that is completely uncorrelated and has very many local optimal peaks - CHAOS

If K remains small while N increases, landscapes retain high accessible local optima As both N and K increase, the height of an increasing number of fitness peaks falls towards the mean fitness: “complexity catastrophe'‘ appears as a result of conflicting constraints among the interdependent choices of the other genes. Those conflicting constraints imply that optimisation can attain only ever poorer compromises. (*) Picture Eve Mitleton-Kelly, Chapter 2 E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (4/11) Properties and insights from the NK model - “Order for Free” and the square root law Consider a network with N genes, each gene can be activated (1) or non-activated (0). A boolean network is a model of N binary genes, where each one receives inputs from other genes and it is governed by a boolean function that defines its state (1 or 0) depending on the activity combination of those network inputs. Example of network random boolean dynamics with 3 genes: K=1; ORDER state - networks with ordered dynamics have few or just a single state cycle attractor to which nearly all of the possible states flow into. # states <proport. growth> #genes K=2; EDGE OF CHAOS - networks with complex dynamics have multiple different basins of attraction with a distribution of sizes, some large, some intermediate, and some small. # states <sqrt growth> #genes K=3 or more; CHAOTIC state - networks with chaotic dynamics have many very cycle attractor separate by small basins of attraction. # states <exp growth> #genes

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (5/11) Properties and insights from the NK model - “Order for Free”, perturbations and power law In a 100,000 node genetic simulation (the approximate number of human genes), the potential set of states is 1030,000. However, for K=2 in the Edge of Chaos, even with random connections and random boolean functions, Kauffman and others found that the model would settle down and cycle through a tiny state cycle with a mere 317 states on it (the sqrt), as it happens in real cells. Perturbations When a single gene of the network is perturbed… K=1; ORDER state – a very little avalanche of damage is observed, the perturbation is damped K=2; EDGE OF CHAOS - avalanches of damage follow a power law – like in the SOC model K=3 or more; CHAOTIC state – avalanches of damage follow an exponential law (butterfly effect)

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

(*) Pictures from Philip Ball, LSE Seminars 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (6/11) Properties and insights from the NK model - “Order for Free”, P-parameter and Biased boolean functions (nature of interactions) P: the fraction of the 2K positions in the Boolean function with either a 1 response or a 0 response, whichever is the larger fraction, P will range from 0.5 to 1.0. The deviation of P above 0.5 measures the internal homogeneity of the Boolean function. (A=5/8) CBF: These functions have at least one input that defines the value of the next value of the regulated gene despite the values of the other inputs. In table – if A is 0, then C will change to 0 despite the input values of A and B. Many real genes use these BBF

The biased degree of the boolean function has been suggested as a measure equivalent to the Strength of Couplings in Social Network Theory (Marion, 1999; Boisot & Child, 1999)

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (7/11) Properties and insights from the NKCS model - Co-evolution between different species in the NK model and SOC: Consider two species with certain coupling between its landscapes. As the first specie searches higher fitness peaks in its fitness landscape, it changes the fitness landscape of the second specie (fly-frog). This co-evolving system present a 2 states of behaviour (order, chaos, and a transition phase) From the simulations it can be seen that through the co-evolutionary dynamics each specie adapt its K towards the transition phase (Edge of chaos) becoming more efficient – showing a power law distribution of avalanches in the extinction events (SOC – Self Organised Criticality). Other examples of co-evolutionary models that exhibit similar avalanche potential laws: Natural extinctions of species in the last 650 mill. years; Power grids outages; Stock economic fluctuations (S&P 500); Traffic fluctuations; Technology and Products growth rates; Organizations growth rates… E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity – The NK model (8/11) Properties and insights from the NKCS model - The effects of C and S: Emergence is a process of adjusting, with its ultimate outcome being the Nash equilibrium. During the emergence stage, species engage in a pre-Nash dance in which they compete for position in the network:

- For K>C, short pre-Nash dance (High K, quickly lock-in in a sub-optimal peak) - For K
E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity (9/11) Properties and insights from other random Boolean network models - The Origin of Auto-catalytic Nets: (…very close to the idea of Small World netwoks) Consider a reaction between two chemicals being catalyzed by a third. A collection of chemicals, where each reaction between two of its number is catalysed by another member of the same collection, is called an auto-catalytic set. Kauffman argues that such auto-catalytic sets are to be expected to occur via natural self-organizational processes. Now imagine strewing a multitude of buttons randomly about a bare floor. Now pick two buttons at random and join them by a thread. Put them back. Choose another two, connect and return them. Continue this process, keeping track of the number of buttons in the largest connected cluster. Kauffman's computer models of this experiment show that this largest connected cluster grows slowly until the number of threads is a little more than half the number of buttons. Then, suddenly, it grows large very quickly. Plotting a graph of maximal cluster size against number of threads yields a steep Scurve. Kauffman calls the resulting graph a reaction network. Kauffman asserts that beyond some level of complexity (critical mass of diversity), autocatalytic sets can be expected to emerge spontaneously, much as the large maximal cluster did in our random graph. On this view, life emerges as a phase transition in sufficiently complex reaction systems. Also seen in Economic networks as a driver of growth creation. E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity (10/11) Conclusions The NK model is a is a simple model (based on homogeneous random Boolean networks) but powerful framework to place different complexity principles in: edge of chaos, degree of connectivity, interdependence, emergence and selforganisation in the creation of new order by auto-catalytic sets, co-evolution and SOC NKCS model, exploration of the space of possibilities and adjacent possibilities, …

It has been applied to several organizational science domains: knowledge, innovation, technology, centralized-decentralized org. forms, modular product and process design, strategy…

It can be useful to analyse the quality of connectivity connections (SN Theory) in terms of the Complexity framework (P-parameter and biased Boolean functions)

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 1. Degree of connectivity (11/11) Some critics “…Every parameter of the NK[C] model is a much simplified approximation of a real world event in a firm. Thus the validity of the model leaves much to be desired. Nevertheless, the NK[C] and other agent based models may offer useful insights about adaptive progression in coevolutionary groups of firms as the models are reformulated to improve their validity”. (McKelvey, “Avoiding Complexity Catastrophe in Coevolutionary Pockets: Strategies for Rugged Landscapes”, ORG SCI 1999) From the IT-Lagecy System Project: “ It should be noted that this kind of modelling has certain limitations. Although the frequency of interactions was studied, the quality of the interactions could not be taken into account (since the connections can have only two values 0 or 1). Consequently, as it stands, the NKCS model cannot account for what the people gain from the interactions and whether their perceptions before and after the discussions are any different. As the issue of the quality of interactions is of the essence in this kind of research, we concluded that the NKCS model, cannot inform our line of investigations, but only to a limited degree.” The P-parameter of the NK model can help to differentiate the strength of couplings but this is not enough. An ABM is necessary to specify more complex cognitive capabilities of the agents and their interrelationships. For example, type of objects in BLANCHE (Noshir Contractor): Attributes: is a numerical value, equation(s), that defines a property of a node over time. A node can have any number of attributes or none at all. Relations: is a set of numerical values that define interactions between nodes. Cognitive Attributes: represent everyone’s view of everyone else’s attributes. Cognitive Relations: represent everyone’s view of every one else’s relations.

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK

index

Levels of Connectivity 1. Degree of connectivity – The NK model 2. Complex networks pattern of connectivity – Small World model 3. Quality of connections – SN theory 4. Future Research Lines

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 2. Complex networks pattern of connectivity – Small World model (1/4) “…Recent studies have revealed a surprising result: the interaction networks displayed by most complex systems are highly heterogeneous (S. H. Strogatz. "Exploring complex networks", Nature 410 (2001) 268-276)… The degree distributions are skewed (i. e. show long tails) so that most nodes are connected to a few ones and a small number are linked to many other units. These distributions are thus very different from the Poissonian shape expected from a simple (Erdos-Renyi) random graph. Different types of networks are observed: from exponential to scale-free (SF) (L. Amaral et al. Proc. Natl. Acad. Sci. USA, 97 (2000) 11149-11152) indicating different basic types of organization. Additionally, complex nets also display the socalled small-world (SW) effect: they are highly clustered (i.e. each node has a well-defined neighborhood of ``close'' nodes) but the minimum distance between any two randomly chosen nodes in the graph is short, a characteristic feature of random graphs (D. J. Watts and S. H. Strogatz. Nature 393 (1998) 440-442)…” (Ricard V. Sole web page about networks, 2003)

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 2. Complex networks pattern of connectivity – Small World model (2/4) “Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes… We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them ‘small-world’ networks, by analogy with the smallworld phenomenon (popularly known as six degrees of separation)” “Procedure: Starting from a ring lattice with n vertices and k edges per vertex, we rewire each edge at random with probability p. This construction allows us to ‘tune’ the graph between regularity (p=0) and disorder (p=1)…” “We quantify the structural properties of these graphs by their characteristic path length L(p) [measures the typical separation between two vertices in the graph (a global property)] and clustering coefficient C(p) [measures the cliquishness of a typical neighborhood (a local property)]”: Regular networks: High clustering (robustness) but low global connectivity (low spread of information…) Random networks: Low clustering but high global connectivity Small world networks: there is a broad interval of p (the introduction of a few long-range edges) over which L(p) is almost as small as Lrandom (high spread of information) yet C(p)>>Crandom (robust). E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

[Watts & Strogatz, 1998] 17

TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 2. Complex networks pattern of connectivity – Small World model (3/4) Properties Most of these SW networks exhibit power law connectivity distribution (LAN Amaral, 2000, Scale Free Networks - AL Barabasi, 1999). They are highly stable under random removal of nodes providing an extraordinary resilience against failure of individual units, but also highly fragile under intentional attack directed to highly-connected nodes (AL Barabasi, 2000).

Examples Collaboration graph of actors, electrical power grid western USA, human language, scientific citation and collaboration networks, social network (6000 M – 6 steps), WWW (1700 M – 19 steps), topology of food webs, cellular and metabolic networks, Zipf law (size and freq. of cities, firms), Pareto law (rent distribution in a country, rent distribution in the world wide)…

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 2. Complex networks pattern of connectivity – Small World model (4/4) In the Social Network Theory, R. Burt “Structural Holes Theory and Social Capital” - shows some implicit drivers/rewards to create this kind of topologies [Burt, 1996, 2000]: Structural holes separate non-redundant contacts/partners, creating bridges and shorter paths Structural hole theory describes how the structure of a network is a competitive advantage for certain people over others People better connected across structural holes are better positioned to broker the flow of information, and unlike exchanges creating entrepreneurial opportunities for third parties

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK

index

Levels of Connectivity 1. Degree of connectivity – The NK model 2. Complex networks pattern of connectivity – Small World model 3. Quality of connections – SN theory 4. Future Research Lines

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 3. The Quality of Connections – Strength of couplings (1/2) Depending on their strength (amount of time, frequency of interaction, emotional intensity, similarity, mutual trusting, reciprocal services…) different properties may arise – SN Theory: Tight couplings (strong ties) within networks facilitate local cohesion, homogeneitycliques and the diffusion and exploitation of codified knowledge

Loose couplings (weak ties) within networks create bridges and shorter paths between non-redundant dissimilar partners, facilitating heterogeneity, novelty and diversity creation (tacit knowledge)

EXPLOITATION DRIVERS:

EXPLORATION DRIVERS:

Current competencies, productivity, efficiency, standardization, optimization of linear processes, best practices, TQM, economies of scale, specialists…

Develop new capabilities, flexibility, ability to change and innovate, generalists…

Both are needed in order to solve the paradox of stability and change (EvE dilemma): Strong ties for the exploitation and maintenance of existing identity, knowledge and practices, with a certain amount of control and coordination (integrated org forms), and weak ties for the exploration of novelty and diversity, innovations and change, agent diversity -The pool of weak ties (Granovetter, 1973) among agents and weak-tie “bridges” across structural holes (Burt 2000)-, with a loosening of control and coordination (dissintegrated org form of autonomous units). Uzzi (1997) shows that the best advantage, the more effective networks within or across groups, comes from an optimal mixing of weak (novelty) and strong ties (efficiency). E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 3. The Quality of Connections – Strength of couplings (2/2) Agents in general may be defined as behaving in a threshold-gate manner - Cohen and Levinthal’s (1990) “absorptive capacity” acts as a threshold gate (capability of absorbing new technical information). High threshold gates turn weak-tie fields into no longer working connections. Nooteboom (2000) relates the concept of absorptive capacity to the “cognitive distance” in the context of effective communication and knowledge diffusion: Outside sources of complementary cognition require a “cognitive distance” which is sufficiently small to allow for understanding (strong ties) but sufficiently large to yield non-redundant, novel knowledge (weak ties).

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK

index

Levels of Connectivity 1. Degree of connectivity – The NK model 2. Complex networks pattern of connectivity – Small World model 3. Quality of connections – SN theory 4. Future Research Lines

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 4. Future Research Lines (1/4) To establish a bridge between the border areas of Complexity, Networks and Organization Sciences Domains. Identify research gaps, as well as search for new insights and synergies within them to extend their theoretical frameworks…

Relationship between the Social Sciences’ Exploration vs. Explotation Org. Cycle , the New Org. Forms Models, and the Complexity NK model relationship, to identify the correct degree of intra&inter-org. connectivity as a function of the environment context.

Relationship between the Social Capital Concept from the Social Theory and the Complexity Small World (SW) Model patterns and dynamics.

Relationship between Social Network Theory strength of couplings, EvE Cycle and Complexity Models (NK and SW models).

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 4. Future Research Lines (2/4) Relationship between the Social Sciences’ Exploration vs. Explotation Org. Cycle , the New Org. Forms Models, and the Complexity NK model relationship, to identify the correct degree of intra&inter-org. connectivity as a function of the environment context.

Exploitation alone leads to an org. becoming better and better at an increasingly obsolescent technology, but is required to survive in the short term. Exploration alone leads to an org. that never realizes the advantages of its discoveries, but is also required to survive in the long term. Exploitation requires the maintenance of existing identity, knowledge and practices, with a certain amount of control and coordination, and exploration requires their change, with a loosening of control and coordination. The EvE Cycle (exploration vs. exploitation cycle) links both Exploration & Exploitation through a path of 5 stages (consolidation, generalization, differentiation, reciprocation, novel combinations) that explains the process of novel structures emergence in the context of Innovation Systems Theory, Theory of Life Cycles and Evolutionary Economics. The EvE Cycle should be analysed under the framework of the Complexity concepts and the NK model in order to profound in its properties and give further insights about its dynamics.

Associated with the different stages of the discovery process there are different entrepreneurial modes: disintegrated forms of organization (decentralized forms - loose couplings/weak ties within network that facilitate diversity, turnover…) perform best in the turbulent stage in which novelty arises, while more integrated forms (centralized forms - tight couplings/strong ties within network that facilitate diffusion and exploitation of knowledge) are best in the stage of consolidation. New Org. Forms balance both opposite dynamics in an unique organizational structure; creating the discontinuities of novel combinations by means of decentralization of autonomous divisions with suffiently weak ties, and to benefit from its advantages of integration, by maintaining a capability for systemic alignment, with strong ties, in the later stages of consolidation and in the stage of generalization. E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 4. Future Research Lines (3/4) Relationship between the Social Capital Concept from the Social Theory and the Complexity Small World (SW) Model patterns and dynamics.

In the Social Network Theory, R. Burt “Structural Holes Theory and Social Capital” states that, in the organizational context, structural holes (weak connections) separate non-redundant contacts/partners, creating bridges and shorter paths. Structural hole theory describes how the structure of a network is a competitive advantage for certain people over others; people better connected across structural holes are better positioned to broker the flow of information, they have higher social capital, creating entrepreneurial opportunities for third parties; and shows some implicit drivers/rewards to create this kind of topologies in the context of Social Sciences.

What Social Network Theory call cliques and bridges, are named as clusters and long-range edges in the SW model. The same network patterns have been identified in both science domains. This coincidence should be explored in further detail.

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK 4. Future Research Lines (4/4) Relationship between Social Network Theory strength of couplings, EvE Cycle and Complexity Models (NK and SW models). Social Network Theory exposes that depending on the quality of connections or strength of couplings (defined as amount of time, frequency of interaction, emotional intensity, similarity, mutual trusting, reciprocal services…) different properties may arise: Tight couplings (strong ties) within networks facilitate local cohesion, homogeneity-cliques and the diffusion and exploitation of codified knowledge. This explains the existence of the clusters found in the SW model. And also can be interpreted as Exploitation Drivers (EvE Cycle), needed for the short term survival; current competencies, productivity, efficiency, standardization, optimization, best practices, economies of scale, specialists… Loose couplings (weak ties) within networks create bridges and shorter paths between non-redundant dissimilar partners, facilitating heterogeneity, exploration of novelty, diversity creation and tacit knowledge. This explains the existence of long-range edges found in the SW model. And also can be interpreted as Exploration Drivers (EvE Cycle), needed for the long term survival; new capabilities, flexibility, ability to change and innovate, generalists…

A first look over these ideas shows that the SW Model network pattern of clusters and long-range edges, from the Complexity Science, has its origins on the necessity of solving the paradox of (short term) stability and (long term) change of the Exploration vs. Exploitation dilemma, and, as the Social Network Theory states, this can be achieved through an optimal mixing of strong ties (cliques – efficiency short term exploitation drivers) and weak ties (structural holes bridges – novelty long term exploration drivers). Further research should be developed.

E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK Main references (1/2) NK model S. Kauffman (1993) “The Origins of Order: Self-Organization and Selection in Evolution”. Oxford University Press S. Kauffman (1995) “At Home in the Universe: The Search for Laws of Self-Organization and Complexity Investigations”. Oxford University Press S. Kauffman (2000) “Investigations”. Oxford University Press B. McKelvey (1999) “Avoiding Complexity Catastrophe in Coevolutionary Pockets: Strategies for Rugged Landscapes”, ORG SCI, Vol. 10 (3)

Small World models L. Amaral et al. (2000) “Classes of behavior of small-world networks” Proc. Natl. Acad. Sci. USA, 97, 11149-11152 A.L. Barabasi., R. A. Albert and H. Jeong (2000) “Error and attack tolerance of complex networks” Nature, 406, 378-382 A. L. Barabasi and R. Albert (1999) “Emergence of Scaling in Random Networks” Science 286, 509-512 R. Burt (2000) “Structural Holes versus Network Closure as Social Capital”, chapter in Social Capital: Theory and Research edited by N. Link, KS Cook and R. Burt. Aldine de Gruyter (2001). See also in Financial Times 5/10/96 “The Social Capital and Entrepreneurial Managers” D. J. Watts and S. H. Strogatz. (1998) “Collective dynamics of small world networks”, Nature 393, 440442 E. Castellano – CONNECTIVITY - LSE Complexity Research Programme Workshop - 15th July, 2003

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TOWARDS AN ORG. CONNECTIVITY FRAMEWORK Main references (2/2) Strength of couplings M.S. Granovetter (1973) “The strength of weak ties”, American Journal of Sociology, Vol 78 (6) B. Uzzi (1997) “Social Structure and The Paradox of Embeddedness”, Administrative Science Quarterly, Vol. 42 (1)

Threshold, absorption capacity, cognitive distance M. Boisot, J. Child (1999) “Organizations as Adaptive Systems in Complex Environments: The Case of China”, ORG SCI, Vol. 10 (3) W.M. Cohen, D.A. Levinthal (1990) “Absorptive Capacity: A Bew Perspective on Learning and Innovation”, Administrative Science Quarterly, Vol. 35 (1) B. Nooteboom, (2000) “Learning and Innovation in Organizations and Economies”, London, Pinter

Other general refs R. Marion (1999) “The Edge of Organization”. SAGE Publications RV Sole web page, nets: http://complex.upf.es/~ricard/complexnets.html

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