Geodesic
Small Stable Generic Graphs with Infinite Weight. Digraphs without Furcations
Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 191-207.

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Grounding on Herwig's generic construction that modifies Hrushovski's construction, we give some examples of small stable theories of digraphs without furcations which have an infinite weight. 
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S. V. Sudoplatov. Small Stable Generic Graphs with Infinite Weight. Digraphs without Furcations. Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 191-207. http://geodesic.mathdoc.fr/item/MT_2007_10_1_a8/

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