GRANDpriv (Graph
Release with Assured
Node Differential
privacy) is an R package that implements a novel method
for privatizing network data using differential privacy. The package
provides functions for generating synthetic networks based on LSM
(Latent Space Model), applying differential privacy to network latent
positions to achieve overall network privatization, and evaluating the
utility of privatized networks through various network statistics. The
privatize and evaluate functions support both LSM and RDPG (Random Dot
Product Graph). For generating RDPG networks, users are encouraged to
use the randnet
package. For more details, see the “proposed method” section of Liu, Bi, and Li (2025).
# Install GRANDpriv from CRAN
install.packages("GRANDpriv")Note: CRAN version is currently under review and not yet available. Please use the development version from GitHub.
# Install devtools if you haven't already
install.packages("devtools")
# Install GRANDpriv from GitHub
devtools::install_github("lsq0000/GRANDpriv")The package requires the following R packages: - EnvStats -
rmutil
- RSpectra - diffpriv - truncnorm - randnet - igraph - HCD -
transport
library(GRANDpriv)
# Generate a sample network using Latent Space Model
# Note: Use larger networks (n >= 1000) for better stability
network <- LSM.Gen(n = 400, k = 2, K = 3, avg.d = 40)
# Privatize the first 200 nodes with different privacy budgets
result <- GRAND.privatize(
A = network$A,
K = 2,
idx = 1:200,
eps = c(1, 2, 5, 10),
model = "LSM"
)
# Evaluate the privatization results
evaluation <- GRAND.evaluate(result)
print(evaluation)
# Evaluate specific statistics only
evaluation_subset <- GRAND.evaluate(result, statistics = c("degree", "triangle"))
print(evaluation_subset)LSM.Gen(n, k, K, avg.d = NULL)Generates a random network following LSM (Latent Space Model) with specified parameters.
n: Integer. Number of nodes
in the network.k: Integer. Dimension of the
latent space.K: Integer. Number of
communities/groups.avg.d: Numeric. Target
average node degree. If NULL, no degree adjustment is performed.Returns: A list containing: - A:
Adjacency matrix of the generated network - g: Graph object
of the generated network - P: Probability matrix of the
generated network - alpha: Node-specific intercept
parameters - Z: Latent positions in k-dimensional space -
idx: Community assignments for each node
GRAND.privatize(A, K, idx, eps = 1, model = "LSM", niter = 500, rho = 0.05, verbose = TRUE)Applies the GRAND (Graph Release with Assured Node Differential privacy) method to privatize network data using differential privacy.
A: Matrix. Adjacency matrix
of the input network.K: Integer. Dimension of the
latent space for network embedding.idx: Integer vector. Indices
of nodes to be privatized.eps: Numeric or numeric
vector. Privacy budget parameter(s) for differential
privacy. Default is 1.model: Character. Model type,
either “LSM” (Latent Space Model) or “RDPG” (Random Dot Product Graph).
Default is “LSM”.niter: Integer. Number of
iterations for the optimization algorithm. Default is 500.rho: Numeric. Parameter
controlling the neighborhood size for conditional distributions. Default
is 0.05.verbose: Logical. Whether to
print progress messages. Default is TRUE.Returns: A list containing: -
non.private.result: Results without privacy (original and
estimated data) - GRAND.result: List with one element per
epsilon value. Each element contains privatization results for that
specific epsilon - Laplace.result: List with one element
per epsilon value. Each element contains baseline Laplace mechanism
results for that specific epsilon - eps: Vector of privacy
budget parameter(s) used
GRAND.evaluate(result, statistics = c("degree", "vshape", "triangle", "eigen", "harmonic"))Evaluates the quality of GRAND privatization results by comparing various network statistics between the original and privatized networks using Wasserstein distance.
result: List. Output from
GRAND.privatize function containing privatization results.statistics: Character vector.
Network statistics to evaluate. Options include: “degree” (Node Degree),
“vshape” (V-Shape Count), “triangle” (Triangle Count), “eigen” (Eigen
Centrality), “harmonic” (Harmonic Centrality). Default is all
statistics.Returns: A data frame containing evaluation results
with columns: - stat: Type of network statistic(s)
evaluated - eps: Privacy budget parameter(s) used -
Hat: Wasserstein distance for release set estimation -
Hat2: Wasserstein distance for holdout set estimation -
GRAND: Wasserstein distance for GRAND privatization method
- Laplace: Wasserstein distance for standard Laplace
mechanism
GRAND uses a two-step approach: 1. Latent Position Estimation: Estimates latent positions from the network structure using either LSM.PGD (Projected Gradient Descent, for LSM) or ASE (Adjacency Spectral Embedding, for RDPG) 2. Multivariate Differential Privacy: Applies DIP (Distribution-Invariant differential Privacy) mechanism to protect latent positions while preserving network utility
GPL (>= 3)
If you use GRANDpriv in your research, please cite:
@misc{liu2025grand,
title={GRAND: Graph Release with Assured Node Differential Privacy},
author={Suqing Liu and Xuan Bi and Tianxi Li},
year={2025},
eprint={2507.00402},
archivePrefix={arXiv},
primaryClass={stat.ML},
url={https://arxiv.org/abs/2507.00402}
}Or in text format:
S. Liu, X. Bi, and T. Li. GRAND: Graph Release with Assured Node Differential Privacy. arXiv preprint arXiv:2507.00402, 2025.Please report issues or contribute to the package through GitHub.