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Table 5 Estimation results for the three largest communities considered from the second level of the hierarchical structure of the Japanese production network

From: Tie-formation process within the communities of the Japanese production network: application of an exponential random graph model

Attributes Community 1 Community 2 Community 3
Endogenous attributes: Θ MLE sig. Θ MLE sig. Θ MLE sig.
Reciprocity 2.50 + 3.52 + 3.31 +
Popularity (k-in-stars) 8.25 + 6.23 + 7.80 +
Activity (k-out-stars) -1.71 + -1.69 + -1.45 +
k-two-paths 0.07 + 0.08 0.07 +
Cyclic closure (AT-C) -0.06 0.39 + -0.19 +
Path closure (AT-T) 0.07 + 0.07 0.08 +
Activity closure (AT-U) 0.05 + -0.17 + 0.05 +
Popularity closure (AT-D) -0.55 + -0.87 + -0.47 +
Exogenous attributes: Θ MLE sig. Θ MLE sig. Θ MLE sig.
Sector homophily -0.42 + -0.33 + 0.41 +
Location homophily 0.65 + 1.27 + 0.37 +
Bank homophily 1.88 + 3.26 + 1.92 +
Size heterophily 1.73.10−09 − 4.18.10−08 − 1.56.10−07 +
Sales heterophily 2.58.10−08 + 5.27.10−08 + 1.56.10−09 +
Sales receiver effect 2.81.10−08 + 5.61.10−08 + 1.76.10−09 +
Sales sender effect − 6.23.10−09 + − 1.86.10−08 + − 5.76.10−10 +
  1. The sizes of communities 1, 2 and 3 are 2,347, 2,249 and 2,173, respectively. A parameter is considered significant for a Wald ratio of ≥ 2. Significance is rejected for a Wald ratio of < 2. The entry in the significance column (sig.) is + if the parameter is significant and otherwise