Does such model exists? I have a problem on distributed graph, with the following model: 
1. There is a Global Graph $G=(V,E)$ 
2. There are $k$ computers. 
3. Each computer $1 \leq i \leq k$ knows ALL the nodes of the graph, i.e. $V$, and subset of the edges, i.e. computer $i$ knows $V_i \subseteq V$. 
4. Each computer observes different subset of edges, i.e., for all $i,j$ : $V_i \cap V_j = \emptyset$. 

I searched for papers which handle the same model, but I didn't find anything. Do you know if such model is being studied?
The model studied in the following work should be a fairly close match with the model that you described (see in particular graph problems "without edge duplication"):


Woodruff &amp; Zhang: "When Distributed Computation is Communication Expensive" http://arxiv.org/abs/1304.4636


See also this work for closely related models:


Klauck et al.: "Distributed Computation of Large-scale Graph Problems" http://arxiv.org/abs/1311.6209


You may also be interested in the "congested clique" model, which is the special case such that $k = |V|$ and computer number $i$ is aware of the edges incident to node number $i$.