# Table 1 Network effects included in the Stochastic Actor-oriented Models

Network effect Equation Visual representation
Outdegree $$\sum\limits_{j} {x_{ij} }$$
Dyadic reciprocity $$\sum\limits_{j} {x_{ij} x_{ji} }$$
Indegree popularity (sqrt) $$\sum\limits_{j} {x_{ij} \sqrt {x_{ + j} } }$$
Outdegree popularity (sqrt) $$\sum\limits_{j} {x_{ij} \sqrt {x_{j + } } }$$
Outdegree activity (sqrt) $$\left( {x_{i + } } \right)^{1.5}$$
Transitive triads $$\sum\limits_{j,h} {x_{ih} x_{ij} x_{jh} }$$
Cyclic triads $$\sum\limits_{j,h} {x_{ij} x_{jh} x_{hi} }$$
Transitive reciprocated triads $$\sum\limits_{j,h} {x_{hi} x_{ih} x_{ij} x_{jh} }$$
GWDSP—mixed-stars $$\sum\limits_{h = 1;h \ne i}^{n} {e^{\alpha } \left\{ {1 - \left( {1 - e^{ - \alpha } } \right)\sum\limits_{j = 1}^{n} {x_{ij} x_{jh} } } \right\}}$$
GWDSP—in-stars $$\sum\limits_{h = 1;h \ne i}^{n} {e^{\alpha } \left\{ {1 - \left( {1 - e^{ - \alpha } } \right)\sum\limits_{j = 1}^{n} {x_{ij} x_{hj} } } \right\}}$$
1. A dotted line represents the creation of a new tie, based on the existing structure of the network as represented by the solid lines
2. i represents Ego, j represents an Alter, and h represents an Alter different from j
3. Xij = 1 if the ordered pair i → j exists (Xij = 0 otherwise)
4. α represents a tuning parameter that may range from 0 to ∞. As recommend by Snijders et al. (2006), α was fixed at 0.69 to model decreasing marginal returns to indirect connections
5. Replacing an index (e.g., j) by a + denotes summation over that index