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Table 1 Network indicators

From: Network analysis for the study of technological collaboration in spaces for innovation. Science and technology parks and their relationship with the university

Indicator

Description

Formula

Degree of centrality

Number of links incident upon a node

\( {C}_d(G)=\frac{{\displaystyle \sum_{i=1}^NCd\left({v}^{*}\right)-Cd(vi)}}{H} \)

CD (g): degree centrality

v * : node with the highest centrality degree

Vi:node i

Index of centralization

The degree to which a network is organized around a point.

\( {C}_d=\frac{{\displaystyle \sum_{i=1}^N\left(C \max - Ci\right)}}{ \max \left[{\displaystyle \sum_{i=1}^N\left(C \max - Ci\right)}\right]} \)

C max :centrality focal node

Ci = centrality rest of nodes

Degree of intermediation

Possibility of a node to mediate between pairs of nodes

\( {C}_b=\frac{2{\displaystyle \sum_{i=1}^g\left[Cb\left({n}^{*}\right)-Cb\left({n}_i\right)\right]}}{\left[\left(g-1\Big){}^2\left(g-2\right)\right)\right]} \)

Cb(n*):highest intermediation between agents

g: number of nodes

Degree of closeness

Average distance of each agent in respect of other agents.

\( {C}_c={\displaystyle \sum_{x\in V-C}df\left(x,C\right)} \)

X:node x

Density

Existing links in relation to possible links.

\( D=\frac{{\displaystyle \sum_{i=1}^N{\displaystyle \sum_{j=1}^NXij}}}{n\left(n-1\right)} \)

Xij: adjacency matrix

N: number of nodes

  1. Source: Borgatti et al. (2002)