# Towards Enhancing the Robustness of Scale-Free IoT Networks by an Intelligent Rewiring Mechanism

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## Abstract

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## 1. Introduction

- Closeness Centrality (CC) measure is utilized to determine the central nodes in the network using minimum computational time.
- An Intelligent Rewiring (INTR) mechanism is proposed to make an optimized SFN using the intelligent selection of nodes.
- Using the global information of nodes, the network is optimized against CC based node removal.
- The Recalculated High Degree based Link Attack (RHDLA) and the High Degree based Link Attack (HDLA) are proposed to affect the network connectivity effectively using the local information of nodes.

## 2. Related Work

## 3. Initialization of Scale-Free Network and Robustness Measure

#### 3.1. Initial Scale-Free Network Construction

Algorithm 1: Construction of an Initial SFN |

Input: A, N, mOutput: $lis{t}_{i}$1: Procedure BA model (A) 2: Random deployment of nodes 3: for all ${n}_{i}\in N$ do4: ${n}_{i}$ broadcast the packet 5: ${n}_{i}\leftarrow Neighbor\text{}Degree\left(\right)$ 6: If $Ni==0$ then7: Make edge with the node that replies first 8: else9: for all $n{e}_{i}\in Ni$ do10: Calculate connection probability 11: Roulette wheel based node selection 12: end for13: end if14: end for15: end procedure16: Update: $lis{t}_{i}$ |

#### 3.2. Robustness Metric

#### 3.3. Closeness Centrality Based Malicious Attacks

Algorithm 2: Evaluate R Against Closeness Centrality Measure |

Input: G, NOutput: MCS, G_{2}, R1: Procedure Centrality Measure (G)2: for all $N\in G$ do3: Find CC of all nodes using Equation (2) 4: Select node having maximum value of CC in G 5: Remove the node and update G to G _{2}6: Calculate R using Equation (1) 7: end for8: end procedure |

#### 3.4. HDLA and RHDLA Based Link Attacks

Algorithm 3: HDLA and RHDLA |

Input: A, E, NOutput: $MCS$1: Procedure High Degree Link Attacks (A)2: for all $E\in G$ do3: Calculate the edge’s degree of whole network as E _{d}4: Sort E _{d}5: Remove max(E _{d})6: Calculate connectivity of the network 7: end for8: end procedure |

#### 3.5. Optimization of Network Using Independent Edges

#### 3.6. INTR Mechanism

Algorithm 4: INTR Mechanism |

Input: N, E, GOutput: R, A1: Procedure INTR Based Edge Rewire (A)2: for all $N\in G$ do3: Find the highest degree node and mark it as i 4: Find the lowest degree neighbor node j based on i 5: Find the second highest degree node and marked k 6: Find the lowest degree neighbor node l based on k 7: Mark edges ij and kl 8: if both edges are independent from E9: Rewire edge (i,k) and edge (j,l) 10: Calculate R 11: Update A and G 12: end if13: end for14: end procedure |

## 4. Simulation Results and Discussion

^{2}as shown in Figure 2. The edge density m of the network is considered as 2. The maximum nodes’ degrees is restricted to 25 by the constraints of nodes while the communication range of each node is 200 m as shown in Figure 2. Table 1 shows solutions for the identified limitations, along with validations. All the simulations are averaged over 10 independent iterations.

#### 4.1. Evaluation of Centrality Measures with Computational Time

#### 4.2. Network Connectivity against Link Attacks

#### 4.3. Robustness against Random and Malicious Attacks

#### 4.4. Centrality Based Node Attacks

#### 4.5. Evaluate the Power-Law Distribution

#### 4.6. Comparison with Existing Algorithms

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Abbreviations and Acronyms | Description |

BA | Barabasi Albert |

BC | Betweenness Centrality |

CC | Closeness Centrality |

DE | Differential Evolution |

EHO | Elephant Herding Optimization |

GA | Genetic Algorithm |

GM | Greedy Model |

HA | Hill Climbing |

HDLA | High Degree based Link Attacks |

INTR | Intelligent Rewiring |

IoT | Internet of Things |

MAs | Malicious Attacks |

MCS | Maximum Connected Subgraphs |

MPGA | Multiple Population Genetic Algorithm |

NCM | Natural Connectivity Model |

RAs | Random Attacks |

R | Robustness |

RHDLA | Recalculated High Degree based Link Attacks |

SA | Simulated Annealing |

SFNs | Scale-Free Networks |

SWNs | Small World Networks |

WSNs | Wireless Sensor Networks |

A | Adjacency matrix of network |

${c}_{x}$ | Closeness of a node x |

$d(y,x)$ | Shortest distance between y and x |

E | Number of edges in graph |

G | Current graph |

${G}_{2}$ | Updated graph |

m | Edge density |

N | Total number of nodes |

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Limitations | Solutions | Validations |
---|---|---|

L1: The BC measure determines the central node in the network inefficiently [17]. | S1: The CC measure determines the network’s central node in less computational time. | V1: The computational time of different centrality measures is evaluated in Figure 3. |

L2: No specific criteria for selection of independent edges [24]. | S2: INTR is proposed to select the independent edges between high and low degree nodes for optimizing the network R. | V2: The R value evaluates the overall performance of network in Figure 8. |

L3: Network is optimized only against high degree node removal [21,25,32]. | S3: Network is optimized against high CC based node removal. | V3: The network performance is evaluated with R values in Figures 5, 7 and 8. |

L4: The network connectivity is affected by link attacks using high computational resources [17]. | S4: Two attacks HDLA and RHDLA are introduced that damage the network effectively. | V4: The network connectivity is validated by performing different centrality based link attacks in Figure 4. |

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**MDPI and ACS Style**

Abbas, S.M.; Javaid, N.; Azar, A.T.; Qasim, U.; Khan, Z.A.; Aslam, S.
Towards Enhancing the Robustness of Scale-Free IoT Networks by an Intelligent Rewiring Mechanism. *Sensors* **2022**, *22*, 2658.
https://doi.org/10.3390/s22072658

**AMA Style**

Abbas SM, Javaid N, Azar AT, Qasim U, Khan ZA, Aslam S.
Towards Enhancing the Robustness of Scale-Free IoT Networks by an Intelligent Rewiring Mechanism. *Sensors*. 2022; 22(7):2658.
https://doi.org/10.3390/s22072658

**Chicago/Turabian Style**

Abbas, Syed Minhal, Nadeem Javaid, Ahmad Taher Azar, Umar Qasim, Zahoor Ali Khan, and Sheraz Aslam.
2022. "Towards Enhancing the Robustness of Scale-Free IoT Networks by an Intelligent Rewiring Mechanism" *Sensors* 22, no. 7: 2658.
https://doi.org/10.3390/s22072658