Degree Of Neighbors Research Articles

The Global Mean First-Passage Time for Degree-Dependent Random Walks in a Class of Fractal Scale-Free Trees

Fractal scale-free structures are widely observed across a range of natural and synthetic systems, such as biological networks, internet architectures, and social networks, providing broad applications in the management of complex systems and the facilitation of dynamic processes. The global mean first-passage time (GMFPT) for random walks on the underlying networks has attracted significant attention as it serves as an important quantitative indicator that can be used in many different fields, such as reaction kinetics, network transport, random search, pathway elaboration, etc. In this study, we first introduce two degree-dependent random walk strategies where the transition probability is depended on the degree of neighbors. Then, we evaluate analytically the GMFPT of two degree-dependent random walk strategies on fractal scale-free tree structures by exploring the connection between first-passage times in degree-dependent random walk strategies and biased random walks on the weighted network. The exact results of the GMFPT for the two degree-dependent random walk strategies are presented and are compared with the GMFPT of the classical unbiased random walk strategy. Our work not only presents a way to evaluate the GMFPT for degree-dependent biased random walk strategies on general networks but also offers valuable insights to enrich the controlling of chemical reactions, network transport, random search, and pathway elaboration.

A new spectral-based index for graphs and its application to polyaromatic compounds

In this study, we introduce a novel index called the modified inverse sum indeg (MISI) energy as an extension of the traditional inverse sum indeg (ISI) energy and neighbor degree sum energy. We devised an algorithm that employs the simplified molecular input line entry system (SMILES) formula of compounds to compute the MISI energy of polycyclic aromatic hydrocarbon (PAH). Additionally, we established the bounds of the MISI energy for certain classes of graphs with fixed number of vertices. A strong correlation between the MISI energy and the total [Formula: see text]-electron energy of PAHs is observed through regression analysis. Remarkably, this correlation outperforms that achieved by the classical ISI energy. These findings highlight the enhanced effectiveness of the MISI energy as a descriptor for capturing significant molecular properties. Moreover, our study establishes a foundation for further theoretical extensions and practical applications in the field of chemical graph theory.

Spatiotemporal Variations in Co-Occurrence Patterns of Planktonic Prokaryotic Microorganisms along the Yangtze River.

Bacteria and archaea are foundational life forms on Earth and play crucial roles in the development of our planet's biological hierarchy. Their interactions influence various aspects of life, including eukaryotic cell biology, molecular biology, and ecological dynamics. However, the coexistence network patterns of these microorganisms within natural river ecosystems, vital for nutrient cycling and environmental health, are not well understood. To address this knowledge gap, we systematically explored the non-random coexistence patterns of planktonic bacteria and archaea in the 6000-km stretch of the Yangtze River by using high-throughput sequencing technology. By analyzing the O/R ratio, representing the divergence between observed (O%) and random (R%) co-existence incidences, and the module composition, we found a preference of both bacteria and archaea for intradomain associations over interdomain associations. Seasons notably influenced the co-existence of bacteria and archaea, and archaea played a more crucial role in spring as evidenced by their predominant presence of interphyla co-existence and more species as keystone ones. The autumn network was characterized by a higher node or edge number, greater graph density, node degree, degree centralization, and nearest neighbor degree, indicating a more complex and interconnected structure. Landforms markedly affected microbial associations, with more complex networks and more core species found in plain and non-source areas. Distance-decay analysis suggested the importance of geographical distance in shaping bacteria and archaea co-existence patterns (more pronounced in spring). Natural, nutrient, and metal factors, including water temperature, NH4+-N, Fe, Al, and Ni were identified as crucial determinants shaping the co-occurrence patterns. Overall, these findings revealed the dynamics of prokaryotic taxa coexistence patterns in response to varying environmental conditions and further contributed to a broader understanding of microbial ecology in freshwater biogeochemical cycling.

An intelligent clustering scheme based on whale optimization algorithm in flying ad hoc networks

Due to the progress of unmanned aerial vehicles (UAVs), this new technology is widely applied in military and civilian areas. Multi-UAV networks are often known as flying ad hoc networks (FANETs). Due to these applications, FANET must ensure communication stability and have high scalability. These goals are achieved by presenting clustering techniques in FANETs. However, the characteristics of these networks, like high-mobility nodes, limited energy, and dynamic topology, have created great challenges in two important processes of clustering protocols, namely cluster construction and the selection of cluster heads. In this paper, an intelligent clustering scheme based on the whale optimization algorithm called ICW is suggested in flying ad hoc networks. Firstly, each UAV specifies its hello interval based on the lifespan of adjacent links to guarantee the adaptability of ICW to FANET. Then, a centralized clustering process is done using a whale optimization algorithm (WOA) to find the best cluster centers on the network. To determine the membership of each UAV in a cluster, ICW employs a new criterion, i.e. closeness ratio, so that each UAV joins a cluster with the best closeness ratio. In addition, the evaluation of each whale is carried out based on a fitness function, consisting of three components, namely the number of isolated clusters, the ratio of inter-cluster distance to intra-cluster distance, and cluster size. Then, a cluster head is selected for each cluster based on a score value. This score is dependent on the weighted sum of four metrics, namely remaining energy, the average link lifespan between each UAV and its neighbors, neighbor degree, and the average distance between each UAV and its neighbors. In the last step, two routing processes, namely intra-cluster routing and inter-cluster routing, are introduced in FANET. Then, the evaluation and implementation of ICW is performed through the NS2 simulator. After completing the simulation process, ICW is compared to MWCRSF, DCM, and GWO, and the evaluation results are presented in two scenarios, namely network evaluation in the clustering process and network evaluation in the routing process. Accordingly, in the first scenario, ICW has low clustering time and a high cluster lifetime. In the second scenario, ICW optimizes energy consumption, network longevity, packet delivery rate, routing overhead, and delay compared to other approaches. However, throughput in ICW is about 3.9% lower than that in MWCRSF.

The bass diffusion model: agent-based implementation on arbitrary networks

ABSTRACT The goal of this study is to model Bass diffusion and its extensions on complex networks, including scale-free networks with arbitrary power-law exponent and assortative degree correlations. For this purpose we employ a combination of the free software packages networkX and NetLogo. Some new results obtained in the agent-based simulations (and differing from those in mean-field approximation) are the following. The introduction of assortative correlations in scale-free networks has the effect of delaying the adoption peak in the Bass model, compared to the uncorrelated case. The peak time depends strongly also on the maximum degree effectively present in the network. For diffusion models with threshold on signed network, a high level of clustering tends to cause adoption blockades. By analysing statistical ensembles of assortative networks generated via Newman rewiring one observes a remarkable strong correlation between the average degree of first neighbours k ˉ nn ( k ) and the average clustering coefficient C ˉ ( k ) .

DCFH: A dynamic clustering approach based on fire hawk optimizer in flying ad hoc networks

In flying ad hoc networks (FANETs), unmanned aerial vehicles (UAVs) communicate with each other without any fixed infrastructure. Because of frequent topological changes, instability of wireless communication, three-dimensional movement of UAVs, and limited resources, especially energy, FANETs deal with many challenges, especially the instability of UAV swarms. One solution to address these problems is clustering because it maintains network performance and increases scalability. In this paper, a dynamic clustering scheme based on fire hawk optimizer (DCFH) is proposed for FANETs. In DCFH, each cluster head calculates the period of hello messages in its cluster based on its velocity. Then, a fire hawk optimizer (FHO)-based dynamic clustering operation is carried out to determine the role of each UAV (cluster head (CH) or cluster member (CM)) in the network. To calculate the fitness value of each fire hawk, a fitness function is suggested based on four elements, namely the balance of energy consumption, the number of isolated clusters, the distribution of CHs, and the neighbor degree. To improve cluster stability, each CH manages the movement of its CMs and adjusts it based on its movement in the network. In the last phase, DCFH defines a greedy routing process to determine the next-hop node based on a score, which consists of distance between CHs, energy, and buffer capacity. Finally, DCFH is simulated using the network simulator version 2 (NS2), and its performance is compared with three methods, including the mobility-based weighted cluster routing scheme (MWCRSF), the dynamic clustering mechanism (DCM), and the Grey wolf optimization (GWO)-based clustering protocol. The simulation results show that DCFH well manages the number of clusters in the network. It improves the cluster construction time (about 55.51%), cluster lifetime (approximately 11.13%), energy consumption (about 15.16%), network lifetime (about 2.6%), throughput (approximately 3.9%), packet delivery rate (about 0.61%), and delay (approximately 14.29%). However, its overhead is approximately 8.72% more than MWCRSF.

A smart filtering-based adaptive optimized link state routing protocol in flying ad hoc networks for traffic monitoring

Nowadays, the use of drones as a fundamental element of smart cities has attracted the attention of many researchers to monitor and control the traffic of vehicles. Because of the high flexibility of multi-drone systems, like flying ad hoc networks (FANETs), they provide various services and improve modern life in smart cities. However, due to the unique features of FANET, especially the high speed of drones and rapid changes in network topology, communication reliability is a serious challenge in this network. Hence, traditional routing protocols, such as optimized link state routing (OLSR) scheme, cannot work well in these networks. In this paper, a smart filtering-based adaptive optimized link state routing (SFA-OLSR) scheme is proposed in FANETs. To increase adaptability to the FANET environment, SFA-OLSR provides a new solution to adjust the hello broadcast period so that each flying node specifies its broadcast period based on a new scale called cosine similarity between real and predicted positions. Furthermore, in SFA-OLSR, each flying node develops a filtering algorithm based on two parameters, namely link lifetime and remaining energy. The purpose of this algorithm is to reduce the size of the single-hop neighboring set of each flying node and minimize the search space when finding multi-point relays (MPRs). This increases the convergence speed of the algorithm. Then, SFA-OLSR exploits the sparrow search algorithm (SSA) to single out the best MPRs. This algorithm introduces a multi-objective function by focusing on three components, including energy, link lifespan, and neighbor degree. Lastly, the simulation process of SFA-OLSR is performed by the NS3 simulator. This process evaluates the performance of the proposed method and three schemes, namely Gangopadhyay et al., P-OLSR, and OLSR-ETX. These evaluations show that SFA-OLSR has a good performance in terms of three scales, namely packet delivery ratio, delay, and throughput, but its overhead is more than other methods.

A Novel Optimized Link-State Routing Scheme with Greedy and Perimeter Forwarding Capability in Flying Ad Hoc Networks

A flying ad hoc network (FANET) is formed from a swarm of drones also known as unmanned aerial vehicles (UAVs) and is currently a popular research subject because of its ability to carry out complicated missions. However, the specific features of UAVs such as mobility, restricted energy, and dynamic topology have led to vital challenges for making reliable communications between drones, especially when designing routing methods. In this paper, a novel optimized link-state routing scheme with a greedy and perimeter forwarding capability called OLSR+GPSR is proposed in flying ad hoc networks. In OLSR+GPSR, optimized link-state routing (OLSR) and greedy perimeter stateless routing (GPSR) are merged together. The proposed method employs a fuzzy system to regulate the broadcast period of hello messages based on two inputs, namely the velocity of UAVs and position prediction error so that high-speed UAVs have a shorter hello broadcast period than low-speed UAVs. In OLSR+GPSR, unlike OLSR, MPR nodes are determined based on several metrics, especially neighbor degree, node stability (based on velocity, direction, and distance), the occupied buffer capacity, and residual energy. In the last step, the proposed method deletes two phases in OLSR, i.e., the TC message dissemination and the calculation of all routing paths to reduce routing overhead. Finally, OLSR+GPSR is run on an NS3 simulator, and its performance is evaluated in terms of delay, packet delivery ratio, throughput, and overhead in comparison with Gangopadhyay et al., P-OLSR, and OLSR-ETX. This evaluation shows the superiority of OLSR+GPSR.

Leverage Centrality on Barycentric Subdivision of Some Graphs

The centrality index on a graph is a real-valued function on the nodes, which provides a ranking of vital nodes in the graph. Each node could be important from an angle, depending on how the concept of importance is defined. There are various measures of centrality, and each one defines a node's importance from a different perspective and provides relevant analytical information about the graph. Leverage centrality of nodes in a graph was defined by Joyce et al. in 2010 as a means to analyze connections within the brain. The definition of this measure shows that it is unique among existing measures in that it counts not just a node's degree, but also its neighbor's degrees. In this paper, we study the leverage centrality of nodes in the $k^{th}$ barycentric subdivision of some classes of graphs. This is a new concept in literature. The process can make regular graphs irregular, and the leverage center of the edge-subdivided graphs under study was investigated.

A Q-learning-based smart clustering routing method in flying Ad Hoc networks

Flying ad hoc networks (FANETs) have particular importance in various military and civilian applications due to their specific features, including frequent topological changes, the movement of drones in a three-dimensional space, and their restricted energy. These features have created challenges for designing cluster-based routing protocols. In this paper, a Q-learning-based smart clustering routing method (QSCR) is suggested in FANETs. In QSCR, each node discovers its neighbors through the periodic exchange of hello messages. The hello time interval is different in each cluster, and cluster leaders determine this interval based on the average speed similarity. Next, an adaptive clustering process is presented for categorizing drones in the clusters. In this step, the cluster leader is selected based on a new parameter called merit value, which includes residual energy, centrality, neighbor degree, speed similarity, and link validity time. Then, a centralized Q-learning model is presented to tune weight coefficients related to merit parameters dynamically. In the last step, the routing process is done using a greedy forwarding technique. Finally, QSCR is run on NS2, and the simulation results of QSCR are compared with those of ICRA, WCA, and DCA. These results show that QSCR carries out the clustering process rapidly but has less cluster stability than ICRA. QSCR gets energy efficiency and improves network lifetime. In the routing process, QSCR has a high packet delivery rate compared to other schemes. Also, the number of isolated clusters created in QSCR is less than other clustering methods. However, the proposed scheme has a higher end-to-end delay than ICRA. Also, this scheme experiences more communication overhead than ICRA slightly.

Planktonic/benthic Bathyarchaeota as a “gatekeeper” enhance archaeal nonrandom co-existence and deterministic assembling in the Yangtze River

Archaea, the third proposed domain of life, mediate carbon and nutrient cycling in global natural habitats. Compared with bacteria, our knowledge about archaeal ecological modes in large freshwater environments subject to varying natural and human factors is limited. By metabarcoding analysis of 303 samples, we provided the first integrate biogeography about archaeal compositions, co-existence networks, and assembling processes within a 6000 km continuum of the Yangtze River. Our study revealed that, among the major phyla, water samples owned a higher proportion of Thaumarchaeota (62.8%), while sediments had higher proportions of Euryarchaeota (33.4%) and Bathyarchaeota (18.8%). A decline of polarization in phylum abundance profile was observed from plateau/mountain/hill to basin/plain areas, which was attributed to the increase of nutrients and metals. Planktonic and benthic Bathyarchaeota tended to co-occur with both major (e.g., methanogens or Thermoplasmata) and minor (e.g., Asgard or DPANN) taxa in the non-random networks, harboring the highest richness and abundances of keystone species and contributing the most positively to edge number, node degree, and nearest neighbor degree. Furthermore, we noted significantly positive contributions of Bathyarchaeota abundance and network complexity to the dominance of deterministic process in archaeal assembly (water: 65.3%; sediments: 92.6%), since higher carbon metabolic versatility of Bathyarchaeota would benefit archaeal symbiotic relations. Stronger deterministic assembling was identified at the lower-reach plain, and higher concentrations of ammonium and aluminum separately functioning as nutrition and agglomerator were the main environmental drivers. We lastly found that the Three Gorges Dam caused a simultaneous drop of benthic Bathyarchaeota abundance, network co-existence, and deterministic effects immediately downstream due to riverbed erosion as a local interference. These findings highlight that Bathyarchaeota are a “gatekeeper” to promote fluvial archaeal diversity, stability, and predictability under varying macroscopic and microscopic factors, expanding our knowledge about microbial ecology in freshwater biogeochemical cycling globally.

Identification of Influential Nodes in Complex Networks With Degree and Average Neighbor Degree

Identifying influential nodes in complex networks is vital for understanding their structure and dynamic behavior. Although methods based on a single characteristic of nodes have been demonstrated to be effective in specific scenarios, the information they provide in dealing with the global aspect of the network is often limited or incomplete. In this paper, we present a measure that combines the degree and the average neighbor degree to evaluate the influence of nodes. As a supplement, we also propose the corresponding gravity index. Experiments on synthetic and real-world networks show that the method proposed in this paper is superior to previous methods based on the single characteristic of nodes in most scenarios. Our gravity strategy is also highly competitive compared with the current famous gravity method.

Measuring the variability of local characteristics in complex networks: Empirical and analytical analysis.

We examine the dynamics for the average degree of a node's neighbors in complex networks. It is a Markov stochastic process, and at each moment of time, this quantity takes on its values in accordance with some probability distribution. We are interested in some characteristics of this distribution: its expectation and its variance, as well as its coefficient of variation. First, we look at several real communities to understand how these values change over time in social networks. The empirical analysis of the behavior of these quantities for real networks shows that the coefficient of variation remains at high level as the network grows. This means that the standard deviation and the mean degree of the neighbors are comparable. Then, we examine the evolution of these three quantities over time for networks obtained as simulations of one of the well-known varieties of the Barabási-Albert model, the growth model with nonlinear preferential attachment (NPA) and a fixed number of attached links at each iteration. We analytically show that the coefficient of variation for the average degree of a node's neighbors tends to zero in such networks (albeit very slowly). Thus, we establish that the behavior of the average degree of neighbors in Barabási-Albert networks differs from its behavior in real networks. In this regard, we propose a model based on the NPA mechanism with the rule of random number of edges added at each iteration in which the dynamics of the average degree of neighbors is comparable to its dynamics in real networks.

Constructing bounded degree graphs with prescribed degree and neighbor degree sequences

Let $D = d_1, d_2, \ldots, d_n$ and $F = f_1, f_2,\ldots, f_n$ be two sequences of positive integers. We consider the following decision problems: is there a $i)$ multigraph, $ii)$ loopless multigraph, $iii)$ simple graph, $iv)$ connected simple graph, $v)$ tree, $vi)$ caterpillar $G = (V,E)$ such that for all $k$, $d(v_k) = d_k$ and $\sum_{w\in \mathcal{N}(v_k)} d(w) = f_k$ ($d(v)$ is the degree of $v$ and $\mathcal{N}(v)$ is the set of neighbors of $v$). Here we show that all these decision problems can be solved in polynomial time if $\max_{k} d_k$ is bounded. The problem is motivated by NMR spectroscopy of hydrocarbons.

Neighbour Degree Connectivity Indices of Graphs and Its Applications to the Octane Isomers

Neighbour Degree Connectivity Indices of Graphs and Its Applications to the Octane Isomers

Neighbors Degree Sum Energy of Commuting and Non-Commuting Graphs for Dihedral Groups

The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer.

Role of degree and weighted coreness based on endpoints in link prediction

Many researchers propose link prediction models based on node similarity. Among all models, researchers found that the endpoint influence plays an important role in evaluating the similarity between endpoints. For endpoint influence, we consider that an endpoint possessing a large and extensive maximum connected subgraph can strongly attract other nodes. After thorough research, we found that the coreness can describe the aggregation degree of neighbors and the endpoint degree may be used to describe the largest connected subgraph of an endpoint. In order to create a model, we repeat our experiments on eight real benchmark datasets after combining endpoint degree and weighted coreness. The experimental results illustrate the positive role of synthetical endpoint degree and weighted coreness for measuring endpoint influence in link prediction.

A new similarity-based link prediction algorithm based on combination of network topological features

In recent years, the study of social networks and the analysis of these networks in various fields have grown significantly. One of the most widely used fields in the study of social networks is the issue of link prediction, which has recently been very popular among researchers. A link in a social network means communication between members of the network, which can include friendships, cooperation, writing a joint article or even membership in a common place such as a company or club. The main purpose of link prediction is to investigate the possibility of creating or deleting links between members in the future state of the network using the analysis of its current state. In this paper, three new similarities, degree neighbor similarity (DNS), path neighbor similarity (PNS) and degree path neighbor Similarity (DPNS) criteria are introduced using neighbor-based and path-based similarity criteria, both of which use graph structures. The results have been tested based on area under curve (AUC) and precision criteria on datasets and it shows well the superiority of the work over the criteria that only use the neighbor or the path.

River networks: An analysis of simulating algorithms and graph metrics used to quantify topology

Abstract River networks are frequently simulated for use in the development and testing of ecological theory. Currently, two main algorithms are used, stochastic branching networks (SBNs) and optimal channel networks (OCNs). The topology of these simulated networks and ‘real’ rivers is often quantified using graph theoretic metrics; however, to date, there has not been a comprehensive analysis of how these algorithms compare regarding graph theoretic metrics, or an analysis of metric redundancy and variability across dendritic ecological networks. We aim to provide guidance as to which algorithm and metrics should be used, and under what circumstances. We performed an extensive simulation study in which we (a) identified orthogonal sets of metrics that describe the topology of real and simulated river networks, (b) analysed the relationship between algorithm hyper‐parameters and node topology metrics, (c) determined whether simulated and real rivers are indistinguishable in their graph metric scores and (d) examined how patterns of species abundances compare across the three network types. We identified two orthogonal sets of node metrics; those that describe centrality and those that describe neighbourhood characteristics. Both stochastic branching networks and optimal channel networks can reproduce network topology metric scores of real rivers, but this relationship is dependent on the algorithm hyper‐parameters used. Finally, using a metapopulation model, we show that both SBNs and OCNs can reproduce ecological patterns of species abundances similar to those of real rivers. SBNs and OCNs can replicate the node topology of real rivers. The choice of which algorithm to use will depend on the research aims, SBNs are faster to generate and more tractable, whereas OCNs can reproduce a wider variety of the characteristics of real rivers, but are more time‐consuming to generate. When quantifying node topology in river networks, we recommend the orthogonal node metrics eccentricity, when interested in network centrality, and mean neighbour degree, when interested in local node importance.

Microbiome network traits in the rumen predict average daily gain in beef cattle under different backgrounding systems

BackgroundBackgrounding (BKG), the stage between weaning and finishing, significantly impacts feedlot performance in beef cattle; however, the contributions of the rumen microbiome to this growth stage remain unexplored. A longitudinal study was designed to assess how BKG affects rumen bacterial communities and average daily gain (ADG) in beef cattle. At weaning, 38 calves were randomly assigned to three BKG systems for 55 days (d): a high roughage diet within a dry lot (DL, n = 13); annual cover crop within a strip plot (CC, n = 13); and perennial pasture vegetation within rotational paddocks (PP, n = 12), as before weaning. After BKG, all calves were placed in a feedlot for 142 d and finished with a high energy ration. Calves were weighed periodically from weaning to finishing to determine ADG. Rumen bacterial communities were profiled by collecting fluid samples via oral probe and sequencing the V4 region of the 16S rRNA bacterial gene, at weaning, during BKG and finishing.ResultsRumen bacterial communities diverged drastically among calves once they were placed in each BKG system, including sharp decreases in alpha diversity for CC and DL calves only (P < 0.001). During BKG, DL calves showed a substantial increase of Proteobacteria (Succinivibrionaceae family) (P < 0.001), which also corresponded with greater ADG (P < 0.05). At the finishing stage, Proteobacteria bloomed for all calves, with no previous alpha or beta diversity differences being retained between groups. However, at finishing, PP calves showed a compensatory ADG, particularly greater than that in calves coming from DL BKG (P = 0.02). Microbiome network traits such as lower average shortest path length, and increased neighbor connectivity, degree, number and strength of bacterial interactions between rumen bacteria better predicted ADG during BKG and finishing than variation in specific taxonomic profiles.ConclusionsBacterial co-abundance interactions, as measured by network theory approaches, better predicted growth performance in beef cattle during BKG and finishing, than the abundance of specific taxa. These findings underscore the importance of early post weaning stages as potential targets for feeding interventions that can enhance metabolic interactions between rumen bacteria, to increase productive performance in beef cattle.