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# Resource Allocation

✓ File Writeback ✕ Property Writeback ✓ Direct Return ✓ Stream Return ✕ Stats

The Topological Link Prediction algorithm employs various metrics to assess the similarity between pairs of nodes, leveraging the topological attributes of nodes. A higher similarity score implies a greater likelihood of future connectivity between two nodes (which are not connected yet).

## Overview

The Resource Allocation algorithm operates under the assumption that nodes transmit resources to each other through their shared neighbors, who act as transmitters. In its basic form, we consider each transmitter possessing a single unit of resource, which is evenly distributed among its neighbors. Consequently, the similarity between two nodes can be gauged by the magnitude of resources that one node transmits to the other. This concept was introduced by Tao Zhou, Linyuan Lü, and Yi-Cheng Zhang in 2009:

It is computed using the following formula:

where N(u) is the set of nodes adjacent to u. For each common neighbor u of the two nodes, the Resource Allocation first calculates the reciprocal of its degree |N(u)|, then sums up these reciprocal values for all common neighbors.

Higher Resource Allocation scores indicate greater similarity between nodes, while a score of 0 indicates no similarity between two nodes.

In this example, N(D) ∩ N(E) = {B, F}, RA(D,E) = $\frac{1}{\mathrm{|N\left(B\right)|}}$ + $\frac{1}{\mathrm{|N\left(F\right)|}}$ = $\frac{1}{4}$ + $\frac{1}{3}$ = 0.5833.

## Considerations

• The Resource Allocation algorithm ignores the direction of edges but calculates them as undirected edges.

## Syntax

• Parameters:
Name
Type
Spec
Default
Optional
Description
ids / uuids []_id / []_uuid / / No ID/UUID of the first set of nodes to calculate; each node in ids/uuids will be paired with each node in ids2/uuids2
ids2 / uuids2 []_id / []_uuid / / No ID/UUID of the second set of nodes to calculate; each node in ids/uuids will be paired with each node in ids2/uuids2
type string Resource_Allocation Adamic_Adar No Type of similarity; for Resource Allocation, keep it as Resource_Allocation
limit int >=-1 -1 Yes Number of results to return, -1 to return all results

## Example

The example graph is as follows:

### File Writeback

Spec Content
filename node1,node2,num
uuids: [3],
uuids2: [1,5,7],
type: 'Resource_Allocation'
}).write({
file:{
filename: 'ra'
}
})

Results: File ra

C,A,0.250000
C,E,0.500000
C,G,0.333333

### Direct Return

Alias Ordinal Type
Description
Columns
0 []perNodePair Node pair and its similarity node1, node2, num
ids: 'C',
ids2: ['A','C','E','G'],
type: 'Resource_Allocation'
}) as ra
return ra

Results: ra

node1 node2 num
3 1 0.25
3 5 0.5
3 7 0.333333333333333

### Stream Return

Alias Ordinal Type
Description
Columns
0 []perNodePair Node pair and its similarity node1, node2, num
find().nodes() as n
with collect(n._id) as nID
ids: 'C',
ids2: nID,
type: 'Resource_Allocation'
}).stream() as ra
where ra.num >= 0.3
return ra

Results: ra

node1 node2 num
3 4 0.583333333333333
3 5 0.5
3 7 0.333333333333333