Figure 1 is an accurate representation of the data.
The goal is to, starting from a random document, take a random number of 
steps to another document. The navigation of the path would be weighted by 
how many inbound edges the metadata object in question has, as well as the 
weight of the individual edge between the document and the metadata object. 

Essentially in your diagram, if I start at "document 4", and I take a 
"random" walk to a metadata object, I will of course go to "metadata 2" 
(the only link possible from document 4). Then, say the weight of the 
(document 3)->(metadata 2) edge is 0.0001, and the weight of the (document 
2)->(metadata 2) edge is 0.721. In most cases I want to then navigate to 
hop to document 2, as it has a much higher edge weight - that's not to say 
that in 30,000 iterations I wouldn't occasionally hop to document 3, 
though! We then generate a random number to see if we continue walking. Say 
we do.

Now that we're at document 2, we start the process over again. BUT, 
document 2 has two metadata properties. Metadata 1 has two edges associated 
with it, and metadata 2 has three edges associated with it. I want to 
weight the decision to move to the random metadata node to be weighted by 
the number of edges connecting to that metadata node. In this case, I want 
to generally weight LESS connected nodes more highly - so in this situation 
we'd slightly prefer hopping to metadata 1 instead of metadata 2. From 
metadata 1, we end up on document 1. We then generate a random number to 
see if we continue walking. Say we don't.

Our weighted random walk might have moved from document 4 -> metadata 2 -> 
document 2 -> metadata 1 -> document 1

In the real graph the number of documents visited could be anywhere from 
1->all of them, in theory

Hopefully this explained what I'm trying to do a little better! :)

If this is too complicated to do as a canned function in orient I think 
that's totally reasonable, someone else is working on writing a more direct 
Java interface which may give us somewhat better control over all this.
Thanks,
Josh

On Wednesday, August 12, 2015 at 1:44:23 AM UTC-7, [email protected] 
wrote:
>
> Hi Josh,
> I did not understand your first question, can you explain what you want to 
> achieve ? 
> What you mean by "centrality of the metadata" ?
> Your structure is like that in Figure 1 or such as that in Figure 2, or 
> neither ?
>
> <https://lh3.googleusercontent.com/-MlpzxEFP5gU/VcsGwpzb2gI/AAAAAAAAAEY/OAFHx7BYuXA/s1600/Image1.png>
>
> <https://lh3.googleusercontent.com/-qHsB19V-5-s/VcsG8yrGRDI/AAAAAAAAAEg/1BJuZqz-b9Y/s1600/Image2.png>
> Alessandro
>

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