Research Article
Predicting the Robustness of Large Real-World Social Networks
Using a Machine Learning Model
Ngoc-Kim-Khanh Nguyen ,
1
Quang Nguyen ,
2,3,4
Hai-Ha Pham,
5
Thi-Trang Le,
4
Tuan-Minh Nguyen,
4
Davide Cassi ,
6,7
Francesco Scotognella,
8,9
Roberto Alferi,
6,7
and Michele Bellingeri
6,7,8
1
Faculty of Basic Science, Van Lang University, Ho Chi Minh, Vietnam
2
Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh 700000, Vietnam
3
Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam
4
John von Neumann Institute, Vietnam National University Ho Chi Minh City, Ho Chi Minh, Vietnam
5
Vietnam National University, International University, Department of Mathematics, Tu Duc, Ho Chi Minh, Vietnam
6
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit` a di Parma, Parco Area Delle Scienze 7/A 43124,
Parma, Italy
7
INFN, Gruppo Collegato di Parma, I-43124 Parma, Italy
8
Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
9
Center for Nano Science and Technology PoliMi, Istituto Italiano di Tecnologia, Via Giovanni Pascoli 70/3, 20133 Milan, Italy
Correspondence should be addressed to Quang Nguyen; nguyenquang29@duytan.edu.vn
Received 30 June 2022; Revised 24 September 2022; Accepted 3 October 2022; Published 9 November 2022
Academic Editor: Andrea Murari
Copyright © 2022 Ngoc-Kim-Khanh Nguyen et al. Tis is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Computing the robustness of a network, i.e., the capacity of a network holding its main functionality when a proportion of its
nodes/edges are damaged, is useful in many real applications. Te Monte Carlo numerical simulation is the commonly used
method to compute network robustness. However, it has a very high computational cost, especially for large networks. Here, we
propose a methodology such that the robustness of large real-world social networks can be predicted using machine learning
models, which are pretrained using existing datasets. We demonstrate this approach by simulating two efective node attack
strategies, i.e., the recalculated degree (RD) and initial betweenness (IB) node attack strategies, and predicting network robustness
by using two machine learning models, multiple linear regression (MLR) and the random forest (RF) algorithm. We use the classic
network robustness metric R as a model response and 8 network structural indicators (NSI) as predictor variables and trained over
a large dataset of 48 real-world social networks, whose maximum number of nodes is 265,000. We found that the RF model can
predict network robustness with a mean squared error (RMSE) of 0.03 and is 30% better than the MLR model. Among the results,
wefoundthattheRDstrategyhasmoreefcacy than IB for attacking real-world social networks. Furthermore, MLR indicates that
the most important factors to predict network robustness are the scale-free exponent α and the average node degree <k>. On the
contrary, the RF indicates that degree assortativity a, the global closeness, and the average node degree <k> are the most important
factors. Tis study shows that machine learning models can be a promising way to infer social network robustness.
1. Introduction
Te study of the social network from a complexity science
perspective has attracted much interest recently [1]. Espe-
cially, the study of dynamic processes that take place in these
complex networks can have various applications. For ex-
ample, the study of network robustness, i.e., “network ro-
bustness” is the capacity of a network to hold its
functionality when a proportion of nodes/edges are re-
moved, can help attack a network efciently, or inversely
Hindawi
Complexity
Volume 2022, Article ID 3616163, 16 pages
https://doi.org/10.1155/2022/3616163