Bipartite (two-mode) networks are ubiquitous. When calculating node centrality measures in bipartite networks, a common approach is to apply PageRank on the one-mode projection of the network. However, the projection can cause information loss and distort the network topology. For better node ranking on bipartite networks, it is preferable to use a ranking algorithm that fully accounts for the topology of both modes of the network.

We present the BiRank package, which implements bipartite ranking algorithms HITS, CoHITS, BGRM, and BiRank. BiRank provides convenience options for incorporating node-level weights into rank estimations, allowing maximum flexibility for different purpose. It can efficiently handle networks with millions of nodes on a single midrange server. Both R and Python versions are available.

CRAN package
with highly efficient functions for estimating various rank (centrality)
measures of nodes in bipartite graphs (two-mode networks) including
HITS, CoHITS, BGRM, and BiRank. Also provides easy-to-use tools for
incorporating or removing edge-weights during rank estimation,
projecting two-mode graphs to one-mode, efficiently estimating PageRank
in one-mode graphs, and for converting edgelists and matrices to
sparseMatrix format. Best of all, the package’s rank estimators can work
directly with common formats of network data including edgelists (class
`data.frame`

, `data.table`

, or
`tbl_df`

) and adjacency matrices (class `matrix`

or `dgCMatrix`

).

This package can be directly installed via CRAN with
`install.packages("birankr")`

. Alternatively, newest versions
of this package can be installed with
`devtools::install_github("BrianAronson/birankr")`

Let’s pretend we have a dataset (`df`

) containing
patient-provider ties (`patient_id`

and
`provider_id`

) among providers that have ever prescribed an
opioid:

```
<- data.frame(
df patient_id = sample(x = 1:10000, size = 10000, replace = T),
provider_id = sample(x = 1:5000, size = 10000, replace = T)
)
```

We are interested in identifying patients who are likely doctor shopping. We assume that a highly central patient in the patient-doctor network is likely to be a person who is deliberately identifying more “generous” opioid prescribers. We therefore estimate a patients’ rank in this network with the CoHITS algorithm:

`<- br_cohits(data = df) df.rank `

Note that rank estimates are scaled according to the size of the network, with more nodes tending to result in smaller ranks. Due to this, it is often advisable to rescale rank estimates more interpretable numbers. For example, we could rescale such that the mean rank = 1 with the following data.table syntax:

```
<- data.table(df.rank)
df.rank := rank/mean(rank)] df.rank[, rank
```

Finally, we decide to identify the IDs and ranks of the highest
ranking patients in `df`

:

`head(df.rank[order(rank, decreasing = T), ], 10)`

For a more detailed example, check out examples/Marvel_social_network.md, where we use the ranking algorithm to analyze the Marvel comic book social network.

Below is a brief outline of each function in this package:

**bipartite_rank**- Estimates any type of bipartite rank.

**br_bgrm**- Estimates ranks with BGRM algorithm

**br_birank**- Estimates ranks with BiRank algorithm

**br_cohits**- Estimates ranks with CoHITS algorithm

**br_hits**- Estimates ranks with HITS algorithm

**pagerank**- Estimates ranks with PageRank algorithm

**project_to_one_mode**- Creates a one mode projection of a sparse matrix

**sparsematrix_from_edgelist**- Creates a sparsematrix from an edgelist

**sparsematrix_from_matrix**- Creates a sparsematrix from a matrix

**sparsematrix_rm_weights**- Removes edge weights from a sparsematrix

Full documentation of `birankr`

can be found in birankr.pdf.

`birankpy`

provides functions for estimating various rank
measures of nodes in bipartite networks including HITS, CoHITS, BGRM,
and BiRank. It can also project two-mode networks to one-mode, and
estimate PageRank on it. `birankpy`

allows user-defined edge
weights. Implemented with sparse matrix, it’s highly efficient.

`networkx`

`pandas`

`numpy`

`scipy`

Install with `pip`

:

`pip install birankpy`

Let’s pretend we have an edge list `edgelist_df`

containing ties between top nodes and bottom nodes:

top_node | bottom_node |
---|---|

1 | a |

1 | b |

2 | a |

… | .. |

123 | z |

To performing BiRank on this bipartite network, just:

```
= birankpy.BipartiteNetwork()
bn
='top_node', bottom_col='bottom_node')
bn.set_edgelist(edgelist_df, top_col
= bn.generate_birank() top_birank_df, bottom_birank_df
```

For a more detailed example, check out examples/Marvel_social_network.ipynb, where we use the ranking algorithm to analyze the Marvel comic book social network.

See documentation for `birankpy`

at birankpy
doc.

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