An Efﬁcient Approach to Enhance the Robustness
of Scale-Free Networks
Syed Minhal Abbas1, Nadeem Javaid1,∗, Muhammad Usman2, Shakira Musa Baig1,
Arsalan Malik1, Anees Ur Rehman1
1Department of Computer Science, COMSATS University Islamabad, Islamabad 44000, Pakistan
2Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad 44000, Pakistan
Email: firstname.lastname@example.org, email@example.com,
Shakira.firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,
∗Corresponding Author: email@example.com; www.njavaid.com
Abstract—In this paper, we aim to increase the robustness
of Scale-Free Networks (SFNs) that are robust against random
attacks; however, they are fragile to malicious attacks. When the
highest-degree nodes are removed from the SFNs, they greatly
affect the connectivity of the remaining nodes. In the proposed
method, we perform two attacks, namely, the high degree link
attacks and the recalculated high degree link attacks. These link
attacks affect the core part of the network. To measure the
extent of damaging the network at a greater portion, we use
the closeness centrality and the eigenvector centrality. The goal
is to construct a topology that shows better robustness against
different malicious attacks with a minimum computational cost.
The Pearson’s correlation coefﬁcient is used to select the measures
that are positively correlated with each other. Based on these
centrality measures, we optimize the network robustness for
both node and link attacks simultaneously. The optimization is
performed based on two efﬁcient measures, which are computa-
tionally less expensive to increase the network robustness.
Index Terms—Scale-free networks, Malicious attack, Robust-
ness, Network topology, Centrality measures, Optimization.
The Internet of Things (IoT) has made remarkable progress
in the last decade. With the increasing number of smart
devices, the digital world is growing rapidly. The IoT allows
manual processes to be automated into the digital world. The
IoT generates the necessary data and includes it in real-time
applications. With the evolution of IoT, its applications are
spread in many ﬁelds, including health system , transporta-
tion system , , medical monitoring system , etc.
In complex network theory, there are mainly two types of
models: the Small World Networks (SWNs) and the Scale-Free
Networks (SFNs) , . The SWNs are constructed by using
heterogeneous nodes. These nodes have different communi-
cation range, energy, and bandwidth. Moreover, the SWNs
contain a small average path length and a high clustering coef-
ﬁcient . Whereas, in SFNs, the degree of nodes is distributed
according to the power law. With this distribution, the high
degree nodes are less in number as compared to low degree
nodes that make connections with similar types of nodes .
On the other hand, the SFNs are constructed by homogeneous
network topologies . The homogeneous nodes have the
same bandwidth and communication range. Therefore, the
network containing the SFNs’ property is usually used in IoT
due to the same bandwidth and transmission range. However,
it is challenging to generate a network topology that is robust
against the malicious attacks , .
Schneider et al.  is introduced a metric to calculate the
robustness R of network against the malicious attacks. The
robustness of the network is calculated as,
In the above equation, s(Q)represents the fraction of
removed nodes, Nrepresents the total number of nodes. The
Rvalue is calculated by analyzing the connectivity of nodes
in a network, which is followed by removing nodes until the
network is damaged. Therefore, we need to make a network
topology that show robustness against the malicious attacks.
Also, the probability of malicious attacks is based on the
intelligent selection of nodes that is growing increasingly ,
The authors in  consider the degree and Betweenness
Centrality (BC) and perform attack on both nodes and links
to evaluate the nodes’ importance. Therefore, when high
degree nodes are attacked, the network breaks down into
sub-networks. In a network, random and malicious attacks
may occur simultaneously. Among them, the malicious attacks
damage the network to a greater extent because they occur on
the most inﬂuential nodes in the network , .
Several strategies are used to make the network robust
against malicious attacks. The SFNs have a high ability to
resist random attacks. However, they are weak against mali-
cious attacks . Therefore, an efﬁcient topology is required
to design the network robust against malicious attacks .
Several optimization techniques including memetic algorithm
, multi-population genetic algorithm , enhanced differ-
ential evolution , natural connectivity model , greedy
model , and elephant herding optimization  are used
to enhance the network robustness. These techniques make the
network onion-like without changing the degree of nodes. The
structure is robust against both random and malicious attacks.
Our contributions in this paper are as follows.
•Two efﬁcient measures, namely, Closeness Centrality
(CC) and Eigenvector Centrality (EC) are used to ﬁnd
out the most inﬂuential nodes in the network with less
•The Pearson’s correlation coefﬁcient is used to determine
the relationship between robustness measures based on
CC and EC and robust the network for both node and
•Two attacks are performed, High Degree Link Attack
(HDLA) and Recalculated HDLA (RHDLA). These at-
tacks help the attacker to affect the network as the greater
portion of the network is damaged in a less time.
The rest of the paper is structured as follows. Section II
contains the related work. The proposed model and description
are discussed in Section III. Section IV explains the simulation
results of our proposed schemes and Section V concludes the
II. RE LATE D WOR K
Previous study uses single-objective optimization with
crossover and mutation. The network that is robust against
node attacks is not necessarily robust against the link attacks
. In the real-world problem, multiple malicious attacks are
not simultaneously considered to optimize the robustness of
a network . Traditional Genetic Algorithm (GA) is used
to make the network robust, premature convergence occurs
due to loss of diversity in the population . Simulated
Annealing (SA) attempts to ﬁnd the best solution with the
worst probability and ﬁnds a better solution, leading to global
optima. The algorithm requires unnecessary comparisons to
optimize the network robustness caused by computational
With the increase of IoT in smart cities, the network is
prone to cyber-attacks that include malicious and random
attacks. The network is required to be robust against cyber-
attacks. However, many redundant operations cause computa-
tional complexity . In , authors use the large SFNs
exploring the hidden features in solution space to enhance the
robustness of the network; however, the computational cost
occurs. The network structure is robust on speciﬁc types of
attacks; however, the structured properties are ignored in a
large complex network , .
Machine Learning (ML) techniques are used to optimize
the network topology against cyber-attacks. SFNs are efﬁcient
regarding robustness against the random attacks; however,
vulnerable to the malicious attacks , . The robust
networks are the essential support for the IoT applications such
as smart cities, intelligent vehicles, smart devices , etc.
However, resource-constrained IoT devices and various types
of attacks are challenging against the network’s robustness
and communication capability . ML-based algorithms are
designed to optimize the network robustness against malicious
attacks. Modiﬁcation of data regarding the swapping edges has
inﬂuenced the structure of the network. Constructing a network
robust to withstand malicious attacks is still a challenging issue
in the optimization problem , .
The robust network against node attacks is not necessarily
strong against the links attack simultaneously . In smart
cities, nodes collect data from different domains . There
is an issue to deal with big data with the network’s robustness
against the malicious attack . GA is used to enhance a
scale-free network’s robustness against malicious attacks as
well as random attacks . Multiple methods are used to
overcome malicious attacks and cascading failures separately
, , . The evolution algorithm is used the two
operators to optimize the network’s tolerance using ﬁxed
probability rates . However, there is an issue in tackling
the large SFN exploring the hidden features in solution space.
Moreover, the improved network structure is based on speciﬁc
types of attacks.
SFNs are tolerant of random attacks; however, prone to
malicious attacks . Fault-tolerant based network topology
evolution scheme is proposed. A new node joins the network
based on preferential attachment and fault probability. Qiu et
al.  propose the scheme that makes the network into the
onion-like structure by performing the degree difference and
angle sum operations. The same degree nodes connect with
each other; however, redundant operations are performed due
to edge swapping. The node’s failure with fault and cyber-
attacks affects the communications among the networks .
Furthermore, some of the nodes in the network are more
interconnected internally as compared with the rest of the
network, thus forming the community.
It is an important feature of the network structure. There-
fore, the network is optimized in each community by con-
sidering the onion-like structure . Therefore, robustness is
enhanced along with the preservation of the network commu-
III. SCA LE -FRE E NET WORKS TOPOLOGY AND
In this section, the proposed system model is designed, as
shown in Fig. 1. In the ﬁgure, three limitations to be addressed
are mapped to the proposed solutions.
A. Construction of Initial Topology
We construct the network using the Barab´
asi Albert (BA)
model . The model generates the SFNs topology by fol-
lowing the power-law distribution. Initially, a network is con-
structed from a small clique. A new node enters in the network
based on the preferential attachment. The node having a high
degree has more probability to be selected by calculating the
degree of the neighboring node through the roulette wheel
mechanism. The communication range and energy resources
of nodes are limited because the high degree nodes consume
more energy, this impacts the overall performance of the
network. Thus, the maximum degree of nodes is limited .
B. Centrality Measures
In the proposed system model, we introduce two measures
CC and EC, to ﬁnd the most inﬂuential nodes in the network.
These measures have less computational cost as compared to
BC. Moreover, CC does not have to determine how many
shortest paths pass through speciﬁc nodes that are required
b) Topology after
b) Topology after
a) Influential Node
L2-Network optimized against
node or link attacks.
L3-Attacker utilizes information
of nodes for attack.
S1-Closeness and eigenvector
S2-Optimized network against
S3-HDLA and RHDLA highly
affect the network.
a) High Degree
Fig. 1. Proposed System Model
The CC measure provides the network’s global information.
It ﬁnds nodes’ centrality based on the relative distance between
each pair of nodes. The centrality of a node ﬁnds the broad-
caster i.e., the communication of one node to all other nodes
is efﬁcient In this process, the shortest distance is calculated
between a speciﬁc node to other nodes in the network.
The CC cof a node xis calculated using the equation
Where drepresents the shortest distance between two ver-
tices yand x.
While, EC measures the importance of nodes in the network.
It assigns a relative score of xto each node. For a given
graph, G= (v, e), the relative score xof EC score a vertex v
connected with other vertex with an edge ecan be deﬁned as:
xv= 1/λ X
Where arepresents the adjacency matrix, vand tare two
vertex, and λis a constant factor .
The EC ﬁnds the node inﬂuencing the entire network and
assigns the relative index value to all nodes based on the
neighbor’s connection. The node containing the high indexed
value contributes more to that node having a low index.
Using the above measures, we ﬁnd the most inﬂuential
nodes in the network to perform the attacks.
C. Centrality Based Malicious Attacks
In the proposed model, three types of malicious attacks
based on degree, CC, and EC are performed. These attacks
affect the functionality of the remaining nodes in the network.
These attacks are performed on both nodes and links. However,
the attacker utilizes the information of high degree nodes
in the network and removes the links. Therefore, in the
proposed system model, we consider two links attacks, namely,
HDLA and RHDLA. In HDLA, the links between two high
degree nodes in the network are removed based on the initial
information. Whereas, in RHDLA the links degree between
two nodes is recalculated after every node’s removal.
D. Optimization of Network Robustness
Our focus is to ﬁnd the robustness of the network with the
limited number of attacks using the provided information from
CC and EC measures , . Based on the robustness mea-
sure for nodes and links, we ﬁnd out the Pearson’s correlation
coefﬁcient among them. The optimization is performed on two
positively correlated measures. The topology that increases the
robustness for both nodes and link attacks is considered an
optimized network topology with less computational cost as
shown in Fig.1. A smart rewiring mechanism is adopted in the
proposed model, that helps to convert the scale-free topology
into an onion-like structure.
In Table 1, L1 section contains a measure to calculate
a node’s centrality using betweenness to make the network
robust. The computational cost to ﬁnd the inﬂuential node
based on the BC is high as compared to the node’s selection
by considering node degree removal , . Two efﬁcient
measures CC and EC ﬁnd the importance of a node in less
time as mentioned in S1 section. Using these measures, we
will construct a network that is efﬁcient against malicious
attacks. Also, it reduces the computational cost and optimizes
the network robustness. In V1 section, the execution time of
CC and EC is validated in Fig. 2. These measures have less
computation time as compared to BC.
The network is optimized on the basis of robustness against
node attack Rnand robustness against link attack Rlin L1
section. Using the proposed centrality measures, we design
a network topology that is fragmented with less number
of attacks. We use Pearson’s correlation coefﬁcient between
Rnand Rl. The positively correlated measures are used to
enhance the network robustness. Various attacks are performed
to strengthen the network, which includes CC, EC, HDLA,
and RHDLA, as explained in S2 section. To enhance network
robustness, we use the smart rewiring mechanism to achieve
the minimum computational cost and faster convergence that
leads to the optimal solution.
MAP PIN G OF LIMITATIONS WITH PROP OS ED SOL UT ION S AN D THE IR VALI DATIO NS .
Limitations Identiﬁed Solutions Proposed Validations
L1: The BC measure increases the compu-
tational cost to ﬁnd the inﬂuential node .
S1: CC and EC ﬁnds the inﬂuential node in
less computational cost.
V1: Validate the execution time with two
centrality measures in Fig. 2.
L2: Network is not robust against different
types of malicious attacks .
S2: Network is optimized simultaneously
against different types of node and link
attacks based on CC, EC, HDLA, and
V2: Network performance is validated with
robustness values in Fig. 4.
L3: Attacker utilizes node’s information to
perform attacks , , , .
S3: Introduce links as well as node attacks. V3: Evaluate the network connectivity by
performing attacks in Fig. 3.
L3 section contains attacks on important nodes , ,
, . Two link attacks, HDLA and RHDLA, based on
the two high degrees nodes are performed on the network, as
explained in S3 section. These attacks will affect the whole
network due to the failure of a high degree edge to make
the network robust. The V3 section evaluates the network
connectivity against different malicious attacks, including BC,
CC, EC, HDLA, and RHDLA.
IV. SIMULATION RESULTS AN D DISCUSSION
SFNs are used to evaluate the efﬁciency of our model with
ROSE and SA algorithms. The simulations are conducted
in MATLAB. In a sensor ﬁeld of 500*500 m2, nodes are
deployed randomly. The modeling process requires each node
to have a limited number of neighbors, and the communication
range r is set at 200m to indicate the communication radius.
In the simulations, the total number of nodes (N) is set to
100, the edge density (m) = 2 and the maximum value of the
node’s degree is 25. We evaluate the results for 100 iterations
in each algorithm. We observe that our model converges to
optimal results within 100 iterations in Fig. 4.
50 100 150 200
Number of Nodes
Execution Time (seconds)
Fig. 2. Comparison of Execution Time between Centrality Measures.
A. Evaluation of Centrality Measures
The comparison of various centrality measures is shown in
Fig. 2, BC the computational overhead of the BC is high. As
compared to BC, CC has a strong ability to ﬁnd the most
important node in less time due to the calculated shortest
distance between two nodes. With the increasing N from 50 to
200 nodes, the closeness measure outperforms the betweenness
measure because CC is not calculated in the shortest paths that
pass only through a speciﬁc node. Furthermore, EC ﬁnds the
0 20 40 60 80 100 120 140 160 180 200
Number of Link Attacks
Probability of Removed Links
Fig. 3. Malicious Link Attacks Affect the Network Topology.
inﬂuential node for the attack in less time as compared to BC.
Because, it indicates not just the direct inﬂuence of a given
node, also the inﬂuence of nodes that are more than a hop
B. Malicious Attacks affect the Network Topology
Validation of the proposed model is achieved through the
removal of links with malicious attacks. Results demonstrate
that the performance of the proposed attacks HDLA and
RHDLA affect the network more as compared to the BC and
CC, as shown in Fig. 3.
With the increasing number of attacks, the probability of
removed links using HDLA and RHDLA is greater than that
of BC and CC attacks. After the 120th attack, HDLA and
RHDLA damage, the network at a greater portion compared
with BC and CC attacks. The effectiveness of HDLA and
RHDLA is shown in Fig. 3. HDLA affects the most important
link between the two high degree nodes.
C. Comparison with Existing Algorithms
The R value of the network is evaluated using the different
number of iterations. Our model, which is smart rewiring
mechanism, is compared with ROSE and SA in Fig. 4.
10 50 100
Number of Iterations
Fig. 4. Robustness value with Different number of Iterations.
With increasing the number of iterations, the proposed smart
rewiring mechanism outperforms both ROSE and SA in terms
of high robustness (i.e., Schneider R-value). Among the best
results, the robustness value for Smart Rewiring, ROSE, and
SA are 0.350 0.289, and 0.259 respectively. As compared to
ROSE and SA schemes, our model’s performance is higher
to make the network robust against malicious attacks. The
process of edge swap is restricted to the high-degree nodes.
In this way, the re-connection of these nodes will change the
overall performance of the network as compared to ROSE and
This paper improves the robustness of SFNs. Two efﬁcient
centrality measures called CC and EC, are used to ﬁnd out the
most inﬂuential nodes in the network. Using these measures,
the malicious attacks are performed. These attacks affect the
network quickly and make it robust. A topology’s robustness
is determined using the Schneider R metric. Two link attacks
are performed, the HDLA and the RHDLA. Both of these
attacks target the high degree links of the network. Simulation
results show that these attacks damage the network with less
computational cost. The network is designed to withstand
malicious attacks on nodes as well as links. Through smart
rewiring, the network topology is turned into an onion-like
structure, which is robust against the malicious attacks.
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