Analyzing consensus algorithms within the context of the ?-nearest ring networks is critical for understanding the efficiency and reliability of large-scale distributed networks. The special properties of the r-nearest neighbor ring offer multiple communication paths, accelerate convergence, and improve the robustness of consensus algorithms. However, this increased connectivity also introduces significant complexity in evaluating the performance of consensus algorithms, since key metrics are typically defined in terms of Laplacian eigenvalues. Especially, estimating the largest eigenvalue of the Laplacian matrix remains a major challenge for the ?-nearest neighbor ring networks. We reformulate the maximization of Laplacian eigenvalue as a minimization of the Dirichlet kernel problem. Firstly, we prove that the first and last lobes of the Dirichlet kernel are the deepest using the shift approach. Next, we apply local smoothness analysis and integer rounding arguments to demonstrate that there is at least one discrete sample to achieve a global minimum in that lobe. This study presents a rigorous analysis to precisely locate and compute the largest eigenvalue, resulting in exact analysis for key performance metrics, including convergence time, first-order network coherence, second-order network coherence, and maximum communication delay, with reduced computational complexity. In addition, our findings illustrate the effect of r in improving the performance of consensus algorithms in large-scale networks.

This paper proposes an efficient method for calculating the eigenvalues of large-scale exponential correlation matrices by leveraging tridiagonal matrix theory. The approach explicitly factorizes the characteristic polynomial into two lower-degree polynomials, preserving the distinction between odd and even matrix orders without resorting to approximations. The ability to efficiently compute these eigenvalues is critical for optimizing channel capacity, transmit beamforming, and other key operations in massive multiple-input multiple-output (MIMO) systems, which are essential for improving data rates, reliability, and spectral efficiency in wireless communications. This work derives the approximate eigenvalues using the Cauchy interlacing theorem. It then validates the accuracy of the proposed eigenvalue expressions by comparing them with existing expressions in the literature and applying them to massive MIMO capacity estimation, showing improved precision

Ranking influential nodes within complex networks offers invaluable insights into a wide array of phenomena ranging from disease management to information dissemination and optimal routing in real-time networking applications. Centrality measures, which quantify the importance of nodes based on network properties and relationships of nodes within the network, are instrumental in achieving this task. These measures are typically classified into local and global centralities. Global measures consider the overall structure and connectivity patterns. However, they often suffer from high computational complexity in large-scale networks. On the other hand, local measures focus on the immediate neighborhood of each node, potentially overlooking global information. To address these challenges, we propose a novel metric called Isolating Clustering Centrality (ISCL), which leverages a convex combination approach. By introducing a convex tuning parameter, ISCL enhances the applicability and adaptability of centrality measures across a wide range of real-world network applications. In this study, we assess the efficacy of the proposed measure using real-world network datasets and simulate the spreading process using susceptible-infected-removed (SIR) and independent cascade (IC) models. Our extensive results demonstrate that ISCL significantly improves spreading efficiency compared to conventional and recent centrality measures, while also maintaining better computational efficiency in large-scale complex networks.

The detection and ranking of influential nodes in complex networks are crucial for various practical applications such as identifying potential drug targets in protein-to-protein interaction networks, critical devices in communication networks, key people in social networks, and transportation hubs in logistics networks. The knowledge of influential spreaders in complex networks is extremely useful for controlling the spread of information. Centrality measures are known for effectively quantifying the influential nodes information in large-scale complex networks. Researchers have proposed different centrality measures in the literature, including Degree, Betweenness, Closeness, and Clustering coefficient centralities. However, these measures have certain limitations when implemented over large-scale complex networks. Most of these measures can be classified as global and local structural approaches. The global structure based algorithms are too complex to evaluate key nodes, particularly in large-scale networks, whereas the local measures overlook the essential global network information. To address these challenges, an extended clustering coefficient local global centrality (ECLGC) is proposed, which combines the local and global structural information to measure the node's influence in large-scale networks. The effectiveness and computational efficiency of the proposed measure are compared with existing centrality measures on real-world network datasets. Susceptible-Infected-Recovered (SIR) model is utilized to evaluate the performance of the ECLGC to capture the high-information dissemination compared to conventional measures. Further, we demonstrate that the proposed measure outperforms the conventional measures in terms of spreading efficiency.

Gossip algorithms are often considered suitable for wireless sensor networks (WSNs) because of their simplicity, fault tolerance, and adaptability to network changes. They are based on the idea of distributed information dissemination, where each node in the network periodically sends its information to randomly selected neighbors, leading to a rapid spread of information throughout the network. This approach helps reduce the communication overhead and ensures robustness against node failures. They have been commonly employed in WSNs owing to their low communication overheads and scalability. The time required for every node in the network to converge to the average of its initial value is called the average time. The average time is defined in terms of the second-largest eigenvalue of a stochastic matrix. Thus, estimating and analyzing the average time required for large-scale WSNs is computationally complex. This study derives explicit expressions of average time for WSNs and studies the effect of various network parameters such as communication link failures, topology changes, long-range links, network dimension, node transmission range, and network size. Our theoretical expressions substantially reduced the computational complexity of computing the average time to Oleft(n{-3}right). Furthermore, numerical results reveal that the long-range links and node transmission range of WSNs can significantly reduce average time, energy consumption, and absolute error for gossip algorithms.

Exploring the significance of popular node’s impact in complex networks yields numerous advantages, such as improving network resilience and accelerating information dissemination. While conventional centrality measures accurately quantify individual node importance, they may inadvertently overlook certain properties of influential nodes. The quest for new centrality metrics has garnered substantial research due to their theoretical relevance and practical applicability in real-world network scenarios. The existing research has predominantly focused on designing centrality metrics based on the local and/or global topological characteristics of nodes. Nevertheless, these metrics do not consider the nodes located in the intermediary zones between the inner and outer regions of a network, resulting in reduced effectiveness when applied to large scale network scenarios. To address these challenges, we have introduced a novel convex framework to formulate the Convex Mixed Centrality (COMC) measure. This metric aims to overcome the limitations of traditional centrality metrics by incorporating insights from both local and global network dynamics, thus enhancing its ability to identify influential nodes across various network regions. To prove the efficacy of our proposed measure, we utilize the Susceptible-Infected-Recovered (SIR) and Independent Cascade (IC) models, alongside the Kendall tau metric. Extensive simulation experiments conducted on various real-world datasets demonstrate that the COMC measure outperforms conventional centrality indices in terms of spreading efficiency, all while maintaining comparable computational complexity. Authors

The detection and ranking of influential nodes remains one of the key areas of research for understanding information diffusion, epidemic control, routing efficiency, and online influence in large-scale complex networks. Centrality measures have been proven to be the most reliable methods that effectively capture the node’s influence in the literature. Based on the structural information incorporated, these measures can be classified as local centrality (PageRank, degree, etc.) and global centrality (betweenness, closeness, etc.) measures. Nevertheless, global measures require huge computational resources in large-scale networks, whereas local measures suffer with less accuracy. To address these challenges, this work proposes a convex combination-based hybrid centrality method. Leveraging the proposed method, we design the six novel centrality metrics, namely convex isolating betweenness centrality (CIBC), convex isolating clustering coefficient centrality (CICLC), convex isolating coreness score centrality (CICRS), convex isolating degree centrality (CIDC), convex isolating eigenvector centrality (CIEC), and convex isolating Katz centrality (CIKC). Next, we compare the effectiveness and computational efficiency of the proposed measures with the traditional and recent measures on the SIR (susceptible–infected–recovered) model using real-world network datasets. Our comprehensive simulations validate the proposed convex centrality measures, showing enhanced spreading efficiency and modest improvements in time complexity

Identifying influential nodes within complex networks holds significant importance for enhancing network resilience and understanding vulnerabilities, thereby providing insights for both theoretical exploration and practical applications. Understanding how quickly information spreads highlights the need to identify influential nodes promptly. Certain global centrality measures, including betweenness (BC), closeness (CC), eigenvector (EC), katz centrality, and coreness score (CR), fail to recognize influential nodes situated near the periphery of the network and those with direct connections to the target node. In response to these challenges and to enhance the influence of identification, we have developed a comprehensive framework, namely ISC, grounded in isolating coefficient, encompassing both a node’s direct connections and those of its neighbors. Using the proposed approach, we defined six new centrality measures, including isolating katz centrality (ISKC), isolating coreness centrality (ISCR), isolating eigenvector centrality (ISEC), isolating betweenness centrality (ISBC), isolating closeness centrality (ISCC), and isolating clustering coefficient centrality (ISCL). Through comparative analysis across five real-world networks, ISC is evaluated alongside existing centrality measures, confirming its effectiveness in identifying influential nodes while maintaining reasonable computational efficiency. The experimental results affirm that ISC outperforms other centrality measures in locating influential nodes within complex networks. Additionally, we evaluate the similarity between our proposed methods and both conventional and recent measures by assessing rank correlations using Kendall’s tau coefficient. The simulation outcomes indicate that one of the proposed methods ISCR, utilizing a lower-complexity algorithm, effectively identifies the most influential nodes with high accuracy. Furthermore, statistical techniques were employed to evaluate the proposed metho...

The increasing number of fake social media accounts poses notable obstacles to the genuineness and legitimacy of virtual conversations, especially during sensitive geopolitical circumstances like the war between Israel and Palestine. In this work, we primarily focus on the activities of fake Twitter profiles during the Israel-Palestine war and use a BERT-based technique for their detection. For text processing and classification, we use BERT, a transformer-based model that has been trained beforehand, by utilizing text data from Twitter. For text processing and classification, we use BERT, a transformer-based model that has been trained beforehand, by utilizing text data from Twitter. To improve classification accuracy, we extract features from textual data using BERT-preprocess and BERT-encoder. This study adds to larger initiatives to counter false information and improve the legitimacy of internet content, especially when it comes to delicate geopolitical situations. Our research provides insights into efficient detection strategies, particularly during crucial global crises, and emphasizes the importance and urgency of tackling the spread of fake profiles on social media platforms.

Plant diseases have become a global concern as they pose a significant threat to food security. These diseases have the potential to cause damage to crops, reduce yields, and compromise food quality. Moreover, the rapid spread of fungi, bacteria, and viruses can lead to widespread crop failures, creating food shortages, price increases, and ultimately, the risk of hunger. However, identifying plant diseases at the early stages remains challenging and time-consuming. Traditional methods of disease identification are often time-consuming and require manual inspection, which slows down timely actions and interventions. In recent years, deep learning-based techniques have shown promising outcomes in the realm of plant disease detection. In this paper, we develop three deep-learning models for the identification of healthy and unhealthy corn plant leaves. The models include a fully convolutional auto-encoder model, and a vision transformer, along with a baseline CNN (Convolutional Neural Network) model. We acquired the data set of corn plant images from UAV drones which were used to train and validate the proposed models. The results indicate that the proposed fully convolutional auto-encoder model achieved an accuracy of 95.09% outperforming both the Vision Transformer and CNN models. By leveraging deep learning-based techniques, such as the fully convolutional auto-encoder model, the agricultural industry can benefit from improved disease detection and prevention. Early and accurate identification of plant diseases allows for timely interventions, such as crop protection measures, which can ultimately safeguard food security

The adverse consequences of crop diseases on agricultural yields are substantial, stemming from their propensity for widespread devastation. To provide precise protection for crops, it becomes essential to employ distinct chemical strategies when addressing various levels of disease intrusion in wheat cultivation. There is an urgent need for a quick and accurate way to assess diseases including leaf blight, loose smut, powdery mildew, and wheat yellow rust disease in order to pursue sustainable agricultural management. Modern remote sensing combined with sophisticated machine learning has sparked a growing interest in determining the severity of these diseases down to the individual leaf level of plants. However, the primary focus of our research is on the widespread field-level detection of wheat crop rust severity using deep learning networks effectively combined with multispectral data analysis from Unmanned Aerial Vehicles (UAVs). The foundation of our work is to provide real-time solution adapted to the sizable dataset gathered from UAV reconnaissance flights. Next, we utilize an approach that is multidimensional and includes the use of several methods such Convolutional Neural Networks (CNNs) and Autoencoders and CNN and Autoencoders integrated with Dense Attention Module (DAM) to train and assess the dataset's capacity to discriminate between various diseases classifications. A comparative analysis of the outcomes demonstrates the noteworthy efficacy of the suggested methodology

Online Social Networks (OSNs) have become ubiquitous platforms for the dissemination of diverse content, en-compassing text, images, and videos. However, the proliferation of fake accounts poses a formidable challenge to the integrity of current OSN systems. Exploiting these fraudulent profiles, malicious actors distribute misleading information, ranging from deceptive surveys to fabricated reports of election rigging and false narratives about the government. Our proposal involves utilizing the latest developments in deep learning, namely in computer vision to address the widespread problem of phony accounts. namely, we suggest implementing an Artificial Neural Network (ANN) and certain Machine Learning methods. Through a series of experiments, our findings reveal a promising outcome, demonstrating superior accuracy and minimal loss when compared to prevalent learning algorithms in the realm of fake account classification. This research contributes to the ongoing discourse on enhancing the robustness of OSN systems against the propagation of misleading information through fake accounts

Over the past decade, there has been extensive research conducted on complex networks, primarily driven by their crucial role in understanding the various real-world networks such as social networks, communication networks, transportation networks, and biological networks. Ranking influential nodes is one of the fundamental research problems in the areas of rumor spreading, disease research, viral marketing, and drug development. Influential nodes in any network are used to disseminate the information as fast as possible. Centrality measures are designed to quantify the node's significance and rank the influential nodes in complex networks. However, these measures typically focus on either the local or global topological structure within and outside network communities. In particular, many measures limit their ability to capture the node's overall impact on small-scale networks. To address these challenges, we develop a novel centrality measure called Isolating Clustering Distance Centrality (ICDC) by integrating the isolating and clustering coefficient centrality measures. The proposed metric gives a more thorough assessment of the node's importance by integrating the local isolation and global topological influence in large-scale complex networks. We employ the SIR and ICM epidemic models to study the efficiency of ICDC against traditional centrality measures across real-world complex networks. Our experimental findings consistently highlight the superior efficacy of ICDC in terms of fast spreading and computational efficiency when compared to existing centrality measures.

The Russo-Ukrainian conflict has been a highly contentious and protracted geopolitical issue that has garnered significant attention on various social media platforms, particularly in Twitter. Online discussion on Twitter has been the main platform for the protracted and polarizing geopolitical conflict between Russia and Ukraine. As the platform generates a lot of user-generated information and allows us to investigate the prospect of using tweets related to the dispute as a method to predict people's personality traits using Twitter posts. To extract and analyse textual information from tweets on the conflict, we used machine learning methods and natural language processing (NLP) approaches in this work. Based on the data that Twitter users shared during the conflict, the main objective of this study is to forecast the personalities of those people. The linguistic and psycholinguistic characteristics were obtained from the preprocessed data and for understanding the personalities we applied Big five factor model (BFFM) on the dataset. With the help of these characteristics and features, the Big Five scores and personality traits are predicted. The machine learning and deep learning algorithms such as Support vector machine (SVM), MLP (Multilayer Perceptron), and RCNN (Region based convolutional neural network) are used to achieve personalities.

Identifying vital nodes involves the task of pinpointing the most essential nodes within intricate networks. This challenge holds significant implications across different domains, including areas like viral marketing and managing the spread of viruses or rumors within real-world networks. Numerous techniques have been proposed for ranking influential nodes in complex networks, spanning from node centrality to diffusion-based processes. K-shell coreness centrality is employed in network analysis to evaluate the structural significance of nodes. The process in-volves k-shell decomposition, which categorizes nodes into shells according to their connectivity patterns. However, these measures are based on the coreness of direct nodes. We proposed an extended coreness score for finding the vital nodes based on the coreness of a node and its neighbors along with the degree. The foundation of degree centrality lies in the principle that the highly connected node is also the most central within the network. With the combination of the degree and isolating centralities, we proposed the isolating extended coreness score. We employ the SIR (Susceptible-Infected-Recovered) model to analyze the maximum information spread achieved by the proposed measure in comparison to conventional centralities. We apply the proposed centrality measure to various real-world networks to identify vital nodes. Additionally, we compare these results with existing basic centrality measures.

Crop diseases pose significant threats to agricultural yields due to their potential for widespread devastation. Precise protection strategies are crucial to address varying disease levels in wheat cultivation, including wheat yellow rust disease, loose smut, powdery mildew, and leaf blight. In the pursuit of sustainable agricultural management, there's a pressing need for a rapid and dependable method to assess these afflictions at the individual plant leaf level. Our research primarily focuses on extensive field-level detection of rust severity in wheat crops using deep learning networks and multispectral data from Unmanned Aerial Vehicles (UAVs). We've developed a real-time solution tailored to vast UAV-collected image datasets. Our multifaceted methodology includes employing Convolutional Neural Networks (CNNs) to distinguish disease categories. Our approach achieves exceptional accuracy, surpassing state-of-the-art models while significantly reducing computational resources by over fifty percent.

In today's world, social networks play a crucial role by providing individuals with a platform to engage, exchange knowledge, and exert influence on others. Finding popular personalities in these networks is important for several purposes, including marketing, information sharing, and opinion forming. To determine influential individuals in social networks, traditional centrality metrics such as degree centrality and betweenness centrality have been extensively used. On the other hand, these measurements usually concentrate on the local or global topological structure both inside and outside of networks. Specifically, a lot of measures restrict their capacity to record the total impact of the node on small-scale networks. To address these challenges, we design a new measure called mixed centrality (MC2) which are focus on the union of the local and global formation of the network. To shown the effectiveness of the proposed measure, we compare the our measures with Degree, Betweenness, Closeness, Cluster-Coefficient, Local and Global centrality measures. We employ the SIR (Susceptible-Infected-Recovered) model to investigate the extreme data dissemination of our centrality metrics compared to traditional measures and to pull off in-depth simulations on big concrete data sets such as jb-pages-company, facebook-combined, jb-pages-public-figure and.fb-pages-government.

The Brain is the controller of the Human system. The unusual growth and partitioning of brain cells lead to a brain tumor which is a severe disease, it's further growth leads to Brain Cancer. The complicatedness of brain tissue demands professional technicians and skillful medical doctors to manually assess and analyze brain tumors using multiple Magnetic Resonance (MR) images with various functionalities, which are the most reliable and secure imaging method that detects every minute object. Brain tumor classification assumes a crucial part in clinical examination and viable treatment. Recently, researchers have shown an increased interest in achieving accurate classification utilizing ML, DL, and neural networks. In this methodology, we plan a strategy for brain tumor characterization utilizing an element of profound features and ML classifiers. In our suggested structure, we support the idea of the SVM strategy and utilized many previously learned deep convolutional neural networks to segregate profound elements from brain MRI images. The filtered significant features are then assessed by a bunch of ML classifiers. Three important profound elements which execute well on a few ML classifiers are selected and collectively form a cluster of deep features which are then taken care of into a few ML classifiers to anticipate the outcome. To inspect the different kinds of previously designed models as ML classifiers, deep feature extractors, and the viability of clustering elements for tumor classification. We utilized 3 distinct brain MRI datasets that are directly accessible from the Kaggle. Trial results display that a group of deep features can assist with further developing execution incredibly, and much of the time, a Support Vector Machine competes with various classifiers, particularly for huge datasets.

Identification of influential vertices plays a very prominent task in a complex network. So, the fundamental task in complex networks is to determine the influential nodes whose expulsion crucially cutoff network harmony. The analysis of the network's topological characteristics, such as susceptibility and resilience, can be aided by identifying influential nodes. This work uses the notion of Maximize the Number of Connected Components Problem, which helps in determining influential nodes, and whose removal yields optimum number of connected components. This work includes application of topology-based centrality measures on real-world networks. However, conventional methods fail to detect most influential nodes that cause the network to split into the optimum number of components. To address this, our work introduces new centrality called global isolating centrality with half of the diameter hops, that focus on network connectedness. The results reveal that the new centrality is better than the existing centralities for certain probability values.

Internet of Things (IoT) is envisioned as a large collection of smart devices that are connected to the Internet and communicate with the goal of realizing a diverse range of applications. These smart devices range from typical home appliances to sophisticated industrial instruments. IoT has numerous applications, such as precision farming, health care, and smart cities. An issue that is prevalent in IoT networks is that due to limited resources, environmental factors, and malicious attacks, some nodes or links fail and adversely affect the functioning of IoT networks. Hence, robustness against the failure of nodes or links is a topic of considerable interest in the area of IoT networks. The robustness of a network is quantified using various spectral graph theoretic measures in network science. One such measure is network criticality which effectively quantifies the robustness against the failure of nodes or communication links. However, this measure can not be used to study the effect of different network parameters for large-scale IoT networks due to huge computational complexity of O(n^{3}). In this work, we derive the explicit formulas of network criticality for IoT networks using r -nearest neighbor graphs and show the effect of nearest neighbors and network size on robustness. Our theoretical expressions substantially reduce the computational complexity as compared to existing graph theory-based metrics. We observe that network robustness decreases with the network size and exponentially increases with nearest neighbors. Our work reduces the time complexity of network criticality evaluation from O(n^{3}) to O(n) for static topologies and to O(1) for switching topologies. Furthermore, we extend our study to random geometric graphs (RGGs) and real-world network data sets. Finally, we study the effect of asymmetric and dynamic topologies on robust IoT networks.

Prism networks belong to generalized petersen graph topologies with planar and polyhedral properties. These networks are extensively used to study the complex networks in the context of computer science, biological networks, brain networks, and social networks. In this letter, the performance analysis of consensus algorithms over prism networks is investigated in terms of convergence time, network coherence, and communication delay. Specifically, in this letter, we first derive the explicit expressions for eigenvalues of Laplacian matrix over m -dimensional prism networks using spectral graph theory. Subsequently, the study of consensus metrics such as convergence time, maximum communication time delay, first order network coherence, and second order network coherence is performed. Our results indicate that the effect of noise and communication time-delay on the consensus dynamics in m -dimensional prism networks is minimal. The obtained results illustrate that the scale-free topology of m -dimensional prism networks along with loopy structure is responsible for strong robustness with respect to consensus dynamics in prism networks.

Agriculture is a very important sector of the Indian economy and this sector has been highly dependent on the efficient usage of water resources. To measure and distribute the exact amount of required water in farm fields is a key problem. To solve this problem, smart sensors can be controlled by different Internet of Things (IoT). In this work, we propose a IoT based hydration system which consists of soil moisture sensor and humidity sensors to know the condition of the soil and aids them in watering the farms accurately. Our hydration system efficiently manages the water usage for farm fields which ensures the saving of water resources. NodeMCU microcontroller has been part of our system. It is programmed to detect moisture, temperature and humidity parameters. Moisture sensor for soil automatically detects the moisture levels in the soil and it alerts us for distributing the water timely. If the water levels are less than the intended levels, then we can remotely turn on the pumping motor and start watering until the moisture level reaches the expected range specified by using the Blynk application. Hence, it will reduce the need of human Labour as water usage.

Internet of Things (IoT) is a powerful data network comprising of various objects such as sensors, radio frequency components, smart appliances, and computers that can be connected via the Internet. The Internet of Everything (IoE) is an evolution of IoT, and it is considered as a combination of data, people, process, and physical devices. Recently, IoE has drawn significant attention from research community due to its wide variety of potential applications. This paper contemplates the studies of state-of-art of IoE, which includes the IoE paradigm, Applications, Challenges, Advantages, and Disadvantages. We also discuss the sensors and the micro-controllers for IoE. This survey article is intended to serve as a guideline for research and development in the IoE.

Internet of Things(IoT) has been immensely progressed through recent years both in academic as well as in the industrial field. IoT has been widely used in Smart Home System(SHS) to provide the wide variety of facilities. In IoT enabled Smart Home environment various things such as lights, home appliances, computers, cameras, and many others which all are connected to the Internet and allowing the user to monitor and control things at any time and from any location. However, we need to ensure the proper security to maintain the quality of the SHS. In this paper, we propose the novel security protocols based on Matrix inversion method to prevent the loss of user data in IoT based SHS. Further, we observe that data transfers within the SHS are protected by an encryption scheme. We use the partition of matrices to larger size matrices over rings for encryption and decryption using matrix inversion method. Data transfers within the SHS more secured in our proposed system.

A dam is a man-made structural barrier built to store and control the flow of water in lakes or rivers. However, mismanagement of dams or extreme weather conditions lead to man-made or natural disasters respectively. Therefore, it is crucial to develop a efficient monitoring systems for maintaining a safe water levels in dams. In this work, we develop an Internet of Things(IoT) based monitoring system to the route the collected flood water dams automatically into the canal. In this system, water level is communicated to the base station using far-field communication. This information will be associated with the cloud and it is monitored by a command center. This command center can take the decision and can furnish the commands to lift the gates simultaneously. The ratio of the distribution of river water from dams to canals will be decided based on several aspects such as command area, water requirement, etc. An integrated system is developed using ARDUINO to meet the above requirements. This paper designs the efficient automated system for dams to effectively manage the water resources and prevent the man-made and natural calamities.

Gossip algorithms have received a lot of attention in recent years due to their ability to compute global statistics using local pair-wise communications. Simple execution, robustness to topology changes, and distributed nature make these algorithms more attractive to wireless sensor network (WSN) applications. Periodic gossip algorithm is a special case of gossip algorithm, where neighbouring nodes gossip at every time instant. Convergence rate plays a fundamental role in effectively measuring the performance of periodic gossip algorithms. However, these algorithms are inherently iterative and estimating their convergence rate for large-scale WSNs is a computationally challenging task. Hence, to utilize the periodic gossip algorithms for sensor networks, it is necessary to study the convergence rate with less computational resources. In this work, we model the WSN as a one-dimensional lattice network and derive the closed form expressions of convergence rate for even and odd number of nodes. To realize the closed-form expressions of convergence rate, we obtain the exact formulas of eigenvalues for pentadiagonal matrices. The numerical analysis reveals the new design insights into the effect of gossip weight, network size, and probability of link failures on the performance of convergence rate. Specifically, we prove that w =0.9 achieves fast convergence rate over w =0.5 for large-scale WSNs. Our theoretical results provide the basic analytical tools for controlling the performance of periodic gossip algorithms in large-scale WSNs.

Deploying a large number of tiny sensor nodes in unattended locations leads to a wide variety of WSN applications in military, environment, health, and disaster management areas. As sensor nodes consist of limited energy resources and recharging them is not possible, it is necessary to design the energyefficient routing protocols. Most of the literature on routing protocols for WSNs can be broadly classified into centralized and distributed protocols. In centralized protocols such as low-energy adaptive clustering hierarchy (LEACH), nodes transmit the data directly to cluster heads. Cluster heads gather the information from all the sensor nodes in the cluster and forwards to the base station. Node failures is a common phenomenon in WSNs. Failure of cluster heads leads to loss of information in that cluster. Hence, centralized protocols are less robust to topology changes due to node failures. To overcome this problem, we can implement distributed algorithms such as average consensus algorithms, where nodes exchange information with only the direct neighbors and calculate the weighted average at every time instant. This process will continue until every node obtains the average of the initial parameter values. Although, this protocol is highly robust to topology changes, it consumes a lot of energy compared to the LEACH protocol. In this work, we compare the energy consumed in the LEACH protocol and the consensus routing protocol and propose an alternative algorithm which is more robust than LEACH and highly energy-efficient than consensus protocol.

Low-energy adaptive clustering hierarchy (LEACH) is a adaptive clustering routing protocol, which is proposed to efficiently manage the energy consumption in Wireless Sensor Networks (WSNs). In this protocol, sensor nodes are organized into clusters and elects the cluster heads randomly. Sensor nodes in each cluster transmit the data directly to the cluster heads. Cluster heads gather the data and transmits to base station. Here, random selection of cluster heads helps to distribute the energy dissipation evenly among all sensor nodes. However, this mechanism consume relatively more energy consumption in large scale WSNs, as the distance between newly elected cluster head and sensor nodes may not be optimal. Intuitively, LEACH protocol with deterministic selection of cluster head based on minimum distance between all sensor nodes in the cluster consumes less energy over random selection. Although, this method increases the life time of the WSN, it is computationally inefficient for large-scale WSNs. In our work, we select the cluster head based on closeness centrality measure. We observe a significant reduction of energy consumption over LEACH protocol with less computational complexity. We also prove that deterministic selection of cluster head based on closeness centrality measure improves the lifetime of WSN significantly over random selection.

Distributed algorithms are extremely useful in wireless sensor network to compute the global statistics using local computations. Periodic gossip algorithm is a distributed consensus algorithm, where neighbouring nodes gossip at every time instant. Convergence rate of periodic gossip algorithms determines the time sensor nodes will take to reach consensus. In this paper, we model the WSN as a r-nearest neighbour network and study the effect of nearest neighbours on convergence rate of the gossip algorithms. The ' r' in nearest neighbour network models the node transmission radius and overhead in wireless sensor networks (WSN). We consider the both even and odd number of nodes and observe the convergence rate drastically increasing with the increase in the number of nearest neighbours until the network is fully connected.