tczzx6/SAGEdata

Real-world community-structured complex networks

Datasets for Discovering hierarchical governing equations for community-structured complex network dynamics (SAGE framework).

This release contains the four real-world networks used to evaluate SAGE. Each network is stored in the same layout so that a single loader works for all of them, and each node's dynamics are known to decompose into a community-level component shared across a group of nodes and an individual-level component unique to that node.

Datasets

Slug	Network	Domain	Nodes N	Steps T	Vars D	Communities K	Time step
urban_mobile_communication	Urban mobile communication (Milan)	Human mobility / communication	48	1008	3	12	10 min
brain_eeg	Brain EEG (PhysioNet S001R01)	Neuroscience	64	2440	2	5	6.25 ms
power_grid	Power grid (IEEE 39-bus New England)	Critical infrastructure	39	5000	1	3	10 ms
urban_rail_transit	Urban rail transit (Beijing)	Transportation	276	1800	2	8	15 min

Sizes above are the released arrays. Three notes on how they relate to the text:

• urban_mobile_communication is shipped at its native 10-minute resolution (1008 steps). The paper aggregated it to 60-minute resolution, giving 168 steps — see scripts/preprocess.py. Supplementary Section 3.1 quotes the aggregated 168.
• urban_rail_transit holds 1800 steps. That is exactly the 25 weekdays in 29 February – 3 April 2016 (2016-02-29 was a Monday) at 18 hours/day and 4 samples/hour. Weekends are absent from the array, although Supplementary Section 3.4 says only "five consecutive weeks".
• power_grid ships one state variable per bus, matching Supplementary Section 3.3. The working copy also held a second array, but it is the central-difference derivative of the first, not an independent observation — see the caveats below.

Layout

dataset_release/
├── README.md                 this file
├── SAGE_datasets.docx        formatted dataset description (for the paper / Zenodo record)
├── data/
│   ├── manifest.json         index of all four datasets
│   ├── urban_mobile_communication/
│   │   ├── x.csv  y.csv  z.csv    states, (T, N), headerless
│   │   ├── adj.csv                adjacency, (N, N), 0/1 integers
│   │   ├── community.csv          node,community
│   │   ├── metadata.json          machine-readable description
│   │   └── README.md              dataset-level description and provenance
│   ├── brain_eeg/
│   ├── power_grid/
│   └── urban_rail_transit/
└── scripts/
    ├── load_dataset.py       unified loader (numpy only)
    ├── preprocess.py         aggregation, Savitzky-Golay smoothing/derivatives, blocked split
    └── build_release.py      regenerates data/ from the raw working copies

File format

Every dataset directory contains exactly the same file names, with the same meaning. T is the number of time steps and N is the number of nodes.

State files — x.csv, y.csv, z.csv ((T, N), headerless CSV)

One file per state variable; a dataset has as many of these as it has state variables (2 or 3). Row t holds the state of all N nodes at time step t; column i holds the complete trajectory of node i. Values are raw observations, in the source dataset's own units.

adj.csv ((N, N), headerless CSV)

Integer adjacency matrix with a zero diagonal. 1 means the two nodes are directly connected in the physical or functional network — transmission line, rail link, spatial grid neighbourhood, or EEG channel coupling, depending on the dataset. See each dataset's README for how the graph was constructed.

community.csv ((N, 2), with header)

Two columns, node and community. Labels are dense integers 0 .. K-1, kept exactly as they appear in the source data so they remain comparable with the original files. K is the number of communities.

metadata.json

Machine-readable form of the same information: slug, title, T, N, D, K, community_sizes, variables (a map from file stem to description), dt, adjacency, source, citation, state_files.

Quick start

pip install numpy scipy

cd dataset_release/scripts
python load_dataset.py     # prints all four datasets with their shapes
python preprocess.py       # smoothing + derivatives + 60/20/20 blocked split

import sys; sys.path.insert(0, "scripts")
from load_dataset import load

ds = load("power_grid")                 # or any slug from the table above
print(ds)                               # <Dataset 'power_grid' T=5000 N=39 D=1 K=3>
x, adj, community = ds.x, ds.adj, ds.community
for k in range(ds.n_communities):
    print(k, ds.community_indices(k).size)

Preprocessing

The release ships raw observational states only. scripts/preprocess.py reproduces the pipeline used in the paper:

1. optional temporal aggregation (mean-pooling, used for the communication data)
2. Savitzky-Golay smoothing along time, which preserves higher-order moments
3. analytic derivatives of the Savitzky-Golay fit
4. a blocked, time-ordered 60 / 20 / 20 train–validation–test split

Splits are always contiguous in time and never shuffled, because temporal order is what makes derivative estimation valid.

Data availability and licensing

The four networks are derived from publicly available sources and are redistributed here under the terms of those sources:

Dataset	Source	Terms
urban_mobile_communication	Telecom Italia Big Data Challenge via the Harvard Dataverse	Open, attribution required (Barlacchi et al., Sci. Data 2, 150055, 2015)
brain_eeg	PhysioNet EEGMMIDB (S001R01)	Open Data Commons Attribution License v1.0
power_grid	IEEE 39-bus New England test system	Public test-system data
urban_rail_transit	Beijing AFC passenger-flow records	Research use; cite Zhang et al., IEEE T-ITS 22, 7004–7014, 2021

Please cite the corresponding source publication for each dataset you use, in addition to the SAGE paper. Full citations are in each dataset's README.md.

Notes and known caveats

• power_grid has one state variable, not two. The working copy held x.csv and y.csv as if they were two observed states. They are not: y equals np.gradient(x, axis=0) / dt to float32 precision (maximum relative residual 4.7e-8), so it is a numerically derived quantity. Only x — the phase state — is released. This agrees with Supplementary Section 3.3, which describes a single state variable per bus. The equation in the main text that relates angle to angular velocity is therefore a relation within the discovered equation, not a statement about the input data. To reproduce the working copy's second array exactly:

  dxdt = np.gradient(ds.x, axis=0) / 0.01     # matches the source y.csv
  

• Adjacency variants for brain_eeg. The working directory held two channel graphs (806 edges each) and two label sets (8 communities and 5). This release ships the 64-channel / 2440-step / 5-community variant described in Supplementary Section 3.2 of the paper.

• urban_rail_transit coverage. Resolved: 1800 steps is exactly the 25 weekdays in the stated range at 18 h/day, 4 samples/hour. Weekends are not in the array. Supplementary Section 3.4 should say "weekdays over five consecutive weeks" rather than "five consecutive weeks" — verify against the source archive.

• urban_mobile_communication step count. Supplementary Section 3.1 reports 168 time steps; the released array is the native 1008-step, 10-minute series that aggregates to 168. The Supplementary text never states the raw resolution.

• Community counts. The paper states K for two datasets only: brain_eeg (five) and power_grid (three). Both match. For urban_rail_transit (8) and urban_mobile_communication (12) the text gives no count; the release uses the labels present in the working copy.