Reciprocity in Directed Hypergraphs: Measures, Findings, and Generators

We provide

• online appendix file
• source code for Sunwoo Kim, Minyoung Choe, Jaemin Yoo, and Kijung Shin. Reciprocity in Directed Hypergraphs: Measures, Findings, and Generators. IEEE ICDM 22.

In this work, we

• Propose a novel hypergraph reciprocity measure, HyperRec.
• Propose an efficient searching algorithm for HyperRec, a Ferret.
• Discover real-world hypergraph's reciprocal pattern on 11 datasets.
• Propose an intuitive reciprocity-preserving hypergraph generator, ReDi, which can captures the reciprocal patterns of real world hypergraphs.

For online appendix, refer to the pdf file named [online_appendix_ICDM22_reciprocity_in_directed_hypergraphs.pdf]

For source codr, refer to the below descriptions.

We provide source codes for following process.

(1) Calculating proposed reciprocity HyperRec of the real-world hypergraphs.
(2) Generating synthetic hypergraphs by using proposed hypergraph generator ReDi, or null hypergraphs & baseline hypergraphs (see main paper for detail).
(3) Reproducing all figures in the paper.

Requirements

To get requirements ready, run the following command on your terminal:

pip install -r requirements.txt

Datasets

We provide 11 real-world hypergraph datasets

• metabolic_iaf1260b
• metabolic_ijo1366
• email_enron
• email_eu
• citation_dm
• citation_software
• qna_math
• qna_server
• bitcoin_2014
• bitcoin_2015
• bitcoin_2016

Please download dataset and put it inside the directory of src folder. For example

src
  |_data 
      |_iaf1260b
      |_ijo1366
      |_ ...
   main_figure.py
   ...

Reproducing Reciprocity and Generation

To obtain results of reciprocity computation and generation, you may use main_reciprocity.py.
Results will be saved in [/result] directory.

main_reciprocity.py [-d NAME_OF_DATASET] [-t TASK] [-a ALPHA_FOR_RECIPROCITY] [-b1 BETA1] [-b2 BETA2] [-in_n NUMBER_OF_INIT_NODES] [-gen_recip DIRECTLY_COMPUTING_RECIPROCITY_AFTER_GENERATION]

optional arguments:
-d NAME_OF_DATASET, Select name of dataset. String type with the exact name of the dataset (See Datasets subsection name).
-t TASK, Select task you want to proceed. String type with one of ["reciprocity", "redi_generation", "null_generation", "base_generation"]
  = "reciprocity" : Computes reciprocity
  = "redi_generation" : Generate ReDi's hypergraph (see main paper for ReDi)
  = "null_generation" : Generate Null hypergraph (see main paper for null hypergraph)
  = "base_generation" : Generate Baseline hypergraph (see main paper for baseline hypergraph)
-a ALPHA, Select alpha parameter. Float type with any alpha value greater than 0. (see main paper for alpha description)
-b1 BETA1, Select beta 1 parameter for ReDi. Float type between [0, 1]. (see main paper for beta1 description)
-b2 BETA2, Select beta 2 parameter for ReDi. Float type between [0, 1]. (see main paper for beta2 description)
-in_n NUMBER_OF_INIT_NODES, Select number of initial nodes parameter x, which implies (initial nodes = x times 2*max(H_{i}, T_{i}))
-gen_recip DIRECTLY_COMPUTING_RECIPROCITY_AFTER_GENERATION, Measuring generated hypergraphs right after the generation. Boolean type 

Reproducing Figures

To obtain figures illustrated in the main paper and online appendix, you may use main_figure.py

As several dataset takes time in generation, we provide result of each generator in [/generated] directory. Please download generated files and put them inside the directory of src folder. For example

src
  |_generated
      |_iaf1260b
      |_ijo1366
      |_ ...
   main_figure.py
   ...

Description regarding running is as follows. Results sill be saved in [/figure] directory.

main_figure.py [-d NAME_OF_DATASET] [-t TASK] 
optional arguments:
-d NAME_OF_DATASET, Select name of dataset. String type with the exact name of the dataset (See Datasets subsection name).
-t TASK, Select task you want to proceed. String type with one of ["obs2", "obs3", "obs2_gen"]
  = "obs2" : Draw observation 2 figure of selected dataset (head-set out degree and tail-set in degree of zero & non-zero reciprocity hyperarcs)
  = "obs3" : Draw observation 3 figure of selected dataset (head-set out degree and tail-set in degree of zero & non-zero reciprocity hyperarcs)
  = "obs2_gen" : Draw observation 3 figure of selected dataset's generated hypergraph (ReDi).