Global technological collaboration network: network analysis of international co-inventions

Abstract

Global innovation networks are emerging as a result of the international division of innovation processes through, among others, international technological collaborations. At the aggregate level, the creation of technological collaboration between countries can be considered as mutually beneficial (or detrimental) and their random distribution is unlikely. Consequently, the dynamics and evolution of the technological collaborations can be expected to fulfil the criteria of a complex network. To study the structure and evolution of the global technological collaboration network, we use patent-based data of international co-inventions and apply the network analysis. In addition, extending the gravity model of international technological collaboration by network measures, we show that a country’s position in the network has very strong impact on the intensity of collaboration with other countries.

Appendix

1.1 Definition and characteristics of a network

A network consists of a graph whose elements include two sets: set of nodes (vertices), that correspond to the selected unit of observation, and a set of lines (lines, relationships), that represent relations between units. A line can be directed – an arc, or undirected—an edge. In a formal way, a network

$$ N = \left( {V,L,W,P} \right) $$

(4)

consists of a graph G = (V, L), where V is the set of nodes, and $L = E \cup A$ is the set of lines, where A is the set of arcs, if the lines are directed, and E is the set of edges, if the lines are not directed. Additional information on the lines is given by the line value function W and on nodes by the value function P.

Regarding the structural properties of a network, network density is a key indicator providing information about the network structure. The density of a network is the number of edges that is expressed as a proportion of the maximum possible number of connections. It is formally defined as

$$ \lambda = \frac{m}{{m_{\hbox{max} } }} $$

(5)

where $m_{\hbox{max} }$ is the total number of lines in a complete network.

Further information on the structure of a network are provided by centrality measures of the network and the nodes (Freeman 1978). In conceptual terms, centrality measures how central an individual is positioned in a network. The most obvious way of capturing degree centrality of V _i is counting the number of its neighbours, i.e. its degree:

$$ C_{i}^{d} = \frac{d}{V - 1} .$$

(6)

The level of centralisation of the entire network, we use a network degree centralisation defined as

$$ C^{d} = \frac{{\sum\nolimits_{i = 1}^{n} {|C_{i}^{d} - C_{i}^{d*} |} }}{(n - 2)\,(n - 1)}, $$

(7)

where $C_{i}^{d*}$ is the highest value of centrality measure in the set of units of a network. Network centralisation index can take any value between 0 (cycle graph), and 1 (star graph).

Regarding the intensity of interactions, the degree measures can be replaced by node strength capturing the sum of weights given to the connections to any V _i . The intensity of connections of vertex i, i.e. its strength is defined as:

$$ s_{i} \equiv \sum\limits_{j \ne i} {w_{ij} } $$

(8)

where w _ij represent the intensity of the directed link from V _i to V _j (Squartini et al. 2011).

Closeness centrality informs how powerful a node is in terms of the shortest paths to others actors of the network (Koschützki et al. 2005). The closeness centrality of a node i is the number of the remaining nodes divided by the sum of all distances between that node and all the remaining ones, i.e.:

$$ C_{i}^{c} = \frac{n - 1}{{\sum\nolimits_{j \ne i}^{n - 1} {\partial_{ij} } }}. $$

(9)

At the aggregate level, centrality closeness of a network is defined as:

$$ C^{c} = \frac{{\sum\nolimits_{i = 1}^{n} {|C_{i}^{c} - C_{i}^{c*} |} }}{(n - 2)\,(n - 1)/(2n - 3)}, $$

(10)

where $C_{i}^{c*}$ is the highest value of closeness centrality measure in the set of units of a network.

Betweenness centrality of a node reflects the amount of control that a node exerts over the interactions of other nodes in the network (Yoon et al. 2006) an is defined as:

$$ C_{i}^{b} = \sum\limits_{j \ne k} {\frac{{\partial_{jk}^{i} }}{{\partial_{jk} }}} , $$

(11)

where $\partial_{jk}^{{}}$ is the total number of shortest paths joining any two nodes V _k and V _j , and $\partial_{jk}^{i}$ is the number of those paths that not only connect V _k and V _j , but also pass through V _i . The betweenness centrality of each node is a number between 0 and 1.

Similarly, the network betweenness centralization index measure can be defined as:

$$ C_{b} = \frac{{\sum\nolimits_{i = 1}^{n} {|C_{i}^{b} - C_{i}^{b*} |} }}{(n - 1)}, $$

(12)

where $C_{i}^{b*}$ is the highest value of betweenness measure among all nodes.

Clustering coefficient reflects the percentage of pairs of node i nearest neighbours that are themselves partners (Watts and Strogatz 1998) and, in undirected networks, the clustering coefficient $C_{i}^{cc}$ of node i is defined as

$$ C_{i}^{cc} = \frac{{2e_{n} }}{{(k_{i} (k_{i} - 1))}} $$

(13)

where k _i is the degree of V _i and e _n is the number of connected pairs between all neighbours of i (Barabasi and Oltvai 2004). The average clustering coefficient of a network is a sum of clustering coefficient values of all nods divided by the total number of nodes in the network. The global clustering coefficient is always a number between 0 and 1, where for a fully connected network CC = 1.

See Tables 3, 4, 5 and 6.

Table 3 Global technological collaboration network indices

Table 4 Countries’ position in the technological collaboration network

Table 5 Descriptive statistics

Table 6 Pair-wise correlations