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Table 2 Formulas for ski(x) selection effects in network x for ego i and alter j, other actors h, and actors’ attributes v. In the actor-oriented modeling framework, network links are directed from clients, who make the procurement decisions, to the suppliers that they select. Dashed arrows signify trading relationships that are likely to be created and maintained if the effect is positive

From: Analyzing the coevolution of interorganizational networks and organizational performance: Automakers’ production networks in Japan

Effect name (Additional description) Mathematical formula Graphical representation
1. Network dynamics
1.1. Endogenous trade network interdependencies
 Network → network
Reciprocity (Favor firms that buy something from our firm) \( {\displaystyle \sum_j{x}_{ij}{x}_{j i}} \)
Preference for firms with partners in common (i.e., firms within the same trading group) Transitive triplets
(Hierarchical cliques)
\( {\displaystyle \sum_{j, h}{x}_{ij}{x}_{j h}{x}_{hi}} \)
Three-cycles (Non-hierarchical cliques) \( {\displaystyle \sum_{j, h}{x}_{j i}{x}_{ih}{x}_{j h}} \)
Common suppliers
(Connect with firms that use the same suppliers)
\( {\displaystyle \sum_j{x}_{ij}}{\displaystyle \sum_{\begin{array}{c}\hfill h\hfill \\ {}\hfill h\ne i, j\hfill \end{array}}\left({b}_0 x-\left|{x}_{ih}-{x}_{j h}\right|\right)} \)
Number of second-tier suppliers
(Connect with multiple primary suppliers through intermediaries)
# [j|x ij  = 0, max(x ih x hj ) > 0]
  Indegree popularity
(Seek the most popular suppliers)
\( {\displaystyle \sum_j{x}_{ij}}{\displaystyle {\sum}_h{x}_{h j}} \)
(Control for network density)
\( {\displaystyle \sum_j{x}_{ij}} \)
1.2. Effects of firms’ performance z on supply network structures
 Performance → network
  Client’s performance
  (High-performing firms connect with more suppliers)
\( {\displaystyle \sum_j{x}_{i j}{z}_i} \)
  Supplier’s performance
  (Selecting high-performing firms as suppliers)
\( {\displaystyle \sum_j{x}_{ij}{z}_j} \)
  Similarity of performance
  (Preference for firms with similar performance)
\( {\displaystyle \sum_j{x}_{ij}\left( si{m}_{ij}^z-\overline{si{m}^z}\right)} \)
2. Performance dynamics
  Linear performance trend
  (Baseline revenue trend)
z i  
  Performance → revenues
   Quadratic performance trend
  (The effect of current performance on the future performance trend)
\( {z}_i^2 \)  
  Network → performance
   (A) Topology:
The effect of the number of suppliers on the future performance trend
\( {z}_i{\displaystyle \sum_j{x}_{i j}} \)
   B Flow:
The effect of the suppliers’ performance on the performance trend
\( {\displaystyle \sum_j{x}_{ij}\left( si{m}_{ij}^z - \overline{si{m}^z}\ \right)} \)
  1. Note: x ij  = 1 if there is a directed tie from i to j and 0 otherwise b \( \overline{si{ m}^z} \) is the mean of all similarity scores, which are defined as \( s i{m}_{i j}^z=\frac{\varDelta -\left|{z}_i-{z}_j\right|}{\varDelta} \) with Δ = max|z i  − z j |