Extremality of degree-based graph entropies

Density-Based Entropy Centrality for Community Detection in Complex Networks

One of the most important problems in complex networks is the location of nodes that are essential or play a main role in the network. Nodes with main local roles are the centers of real communities. Communities are sets of nodes of complex networks and are densely connected internally. Choosing the right nodes as seeds of the communities is crucial in determining real communities. We propose a new centrality measure named density-based entropy centrality for the local identification of the most important nodes. It measures the entropy of the sum of the sizes of the maximal cliques to which each node and its neighbor nodes belong. The proposed centrality is a local measure for explaining the local influence of each node, which provides an efficient way to locally identify the most important nodes and for community detection because communities are local structures. It can be computed independently for individual vertices, for large networks, and for not well-specified networks. The use of the proposed density-based entropy centrality for community seed selection and community detection outperforms other centrality measures.

Potential long consequences from internal and external ecology: loss of gut microbiota antifragility in children from an industrialized population compared with an indigenous rural lifestyle

Human health is strongly mediated by the gut microbiota ecosystem, which, in turn, depends not only on its state but also on its dynamics and how it responds to perturbations. Healthy microbiota ecosystems tend to be in criticality and antifragile dynamics corresponding to a maximum complexity configuration, which may be assessed with information and network theory analysis. Under this complex system perspective, we used a new analysis of published data to show that a children's population with an industrialized urban lifestyle from Mexico City exhibits informational and network characteristics similar to parasitized children from a rural indigenous population in the remote mountainous region of Guerrero, México. We propose then, that in this critical age for gut microbiota maturation, the industrialized urban lifestyle could be thought of as an external perturbation to the gut microbiota ecosystem, and we show that it produces a similar loss in criticality/antifragility as the one observed by internal perturbation due to parasitosis by the helminth A. lumbricoides. Finally, several general complexity-based guidelines to prevent or restore gut ecosystem antifragility are discussed.

Degree-Based Graph Entropy in Structure-Property Modeling

Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose dG(vi) is degree of the vertex vi for each i=1,2,…,n. Now, the k-th degree-based graph entropy for G is defined as Id,k(G)=-∑i=1ndG(vi)k∑j=1ndG(vj)klogdG(vi)k∑j=1ndG(vj)k, where k is real number. The first-degree-based entropy is generated for k=1, which has been well nurtured in last few years. As ∑j=1ndG(vj)k yields the well-known graph invariant first Zagreb index, the Id,k for k=2 is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of Id,2 in structure property modeling of molecules.

Extremal values of VDB topological indices over F-benzenoids with equal number of edges

The utilization of molecular structure topological indices is currently a standing operating procedure in the structure-property relations research, especially in QSPR/QSAR study. In the past several year, generous molecular topological indices related to some chemical and physical properties of chemical compounds were put forward. Among these topological indices, the VDB topological indices rely only on the vertex degree of chemical molecular graphs. The VDB topological index of an $ n $-order graph $ G $ is defined as TI(G) = \sum\limits_{1\leq i\leq j\leq n-1}m_{ij}\psi_{ij}, $ where $ \{\psi_{ij}\} $ is a set of real numbers, $ m_{ij} $ is the quantity of edges linking an $ i $-vertex and another $ j $-vertex. Numerous famous topological indices are special circumstance of this expression. f-benzenoids are a kind of polycyclic aromatic hydrocarbons, present in large amounts in coal tar. Studying the properties of f-benzenoids via topological indices is a worthy task. In this work the extremum $ TI $ of f-benzenoids with given number of edges were determined. The main idea is to construct f-benzenoids with maximal number of inlets and simultaneously minimal number of hexagons in $ \Gamma_{m} $, where $ \Gamma_{m} $ is the collection of f-benzenoids with exactly $ m $ $ (m\geq19) $ edges. As an application of this result, we give a unified approach of VDB topological indices to predict distinct chemical and physical properties such as the boiling point, $ \pi $-electrom energy, molecular weight and vapour pressure etc. of f-benzenoids with fixed number of edges.

Computing the Entropy Measures for the Line Graphs of Some Chemical Networks

Chemical Graph entropy plays a significant role to measure the complexity of chemical structures. It has explicit chemical uses in chemistry, biology, and information sciences. A molecular structure of a compound consists of many atoms. Especially, the hydrocarbons is a chemical compound that consists of carbon and hydrogen atoms. In this article, we discussed the concept of subdivision of chemical graphs and their corresponding line chemical graphs. More preciously, we discuss the properties of chemical graph entropies and then constructed the chemical structures namely triangular benzenoid, hexagonal parallelogram, and zigzag edge coronoid fused with starphene. Also, we estimated the degree-based entropies with the help of line graphs of the subdivision of above mentioned chemical graphs.

On eccentricity-based entropy measures for dendrimers

The eccentricity-based entropy inspired by Shannon's entropy approach is the information-theoretic quantity to figure out the structural information of complex networks. The investigation for advance biomedical utilization of dendrimers has improved the synthesis of radical based molecules. Categorically, attaining radical dendrimers has initiated their use in different fields such as anti-tumor agents and as magnetic resonance imaging. The use of radical dendrimers has increased the possibility of establishing new kinds of devices based on para-magnetic axioms of organic radicals. In this article, we discussed dendrimer based on cyclotriphosphazene ( N 3 P 3 ) which has balanced edge groups and these are examined by EPR temperature spectrum. Firstly, we computed eccentricity-based indices and then we computed eccentricity based entropies by developing an acquaintance between these indices and their entropies. Moreover we presented our computed result numerically and graphically which leads to good importance of our contribution.

Eigenvalue-based entropy in directed complex networks

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs

The BC-subtree (a subtree in which any two leaves are at even distance apart) number index is the total number of non-empty BC-subtrees of a graph, and is defined as a counting-based topological index that incorporates the leaf distance constraint. In this paper, we provide recursive formulas for computing the BC-subtree generating functions of multi-fan and multi-wheel graphs. As an application, we obtain the BC-subtree numbers of multi-fan graphs, r multi-fan graphs, multi-wheel (wheel) graphs, and discuss the change of the BC-subtree numbers between different multi-fan or multi-wheel graphs. We also consider the behavior of the BC-subtree number in these structures through the study of extremal problems and BC-subtree density. Our study offers a new perspective on understanding new structural properties of cyclic graphs.

Twenty Years of Entropy Research: A Bibliometric Overview

Entropy, founded in 1999, is an emerging international journal in the field of entropy and information studies. In the year of 2018, the journal enjoyed its 20th anniversary, and therefore, it is quite reasonable and meaningful to conduct a retrospective as its birthday gift. In accordance with Entropy’s distinctive name and research area, this paper creatively provides a bibliometric analysis method to not only look back at the vicissitude of the entire entropy topic, but also witness the journal’s growth and influence during this process. Based on 123,063 records extracted from the Web of Science, the work in sequence analyzes publication outputs, high-cited literature, and reference co-citation networks, in the aspects of the topic and the journal, respectively. The results indicate that the topic now has become a tremendous research domain and is still roaring ahead with great potentiality, widely researched by different kinds of disciplines. The most significant hotspots so far are suggested as the theoretical or practical innovation of graph entropy, permutation entropy, and pseudo-additive entropy. Furthermore, with the rapid growth in recent years, Entropy has attracted many dominant authors of the topic and experiences a distinctive geographical publication distribution. More importantly, in the midst of the topic, the journal has made enormous contributions to major research areas, particularly being a spear head in the studies of multiscale entropy and permutation entropy.

Modeling and Fusing the Uncertainty of FMEA Experts Using an Entropy-Like Measure with an Application in Fault Evaluation of Aircraft Turbine Rotor Blades

As a typical tool of risk analysis in practical engineering, failure mode and effects analysis (FMEA) theory is a well known method for risk prediction and prevention. However, how to quantify the uncertainty of the subjective assessments from FMEA experts and aggregate the corresponding uncertainty to the classical FMEA approach still needs further study. In this paper, we argue that the subjective assessments of FMEA experts can be adopted to model the weight of each FMEA expert, which can be regarded as a data-driven method for ambiguity information modeling in FMEA method. Based on this new perspective, a modified FMEA approach is proposed, where the subjective uncertainty of FMEA experts is handled in the framework of Dempster–Shafer evidence theory (DST). In the improved FMEA approach, the ambiguity measure (AM) which is an entropy-like uncertainty measure in DST framework is applied to quantify the uncertainty degree of each FMEA expert. Then, the classical risk priority number (RPN) model is improved by aggregating an AM-based weight factor into the RPN function. A case study based on the new RPN model in aircraft turbine rotor blades verifies the applicable and useful of the proposed FMEA approach.

Relating Vertex and Global Graph Entropy in Randomly Generated Graphs

Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically.

An Extension to Deng's Entropy in the Open World Assumption with an Application in Sensor Data Fusion

Quantification of uncertain degree in the Dempster-Shafer evidence theory (DST) framework with belief entropy is still an open issue, even a blank field for the open world assumption. Currently, the existed uncertainty measures in the DST framework are limited to the closed world where the frame of discernment (FOD) is assumed to be complete. To address this issue, this paper focuses on extending a belief entropy to the open world by considering the uncertain information represented as the FOD and the nonzero mass function of the empty set simultaneously. An extension to Deng’s entropy in the open world assumption (EDEOW) is proposed as a generalization of the Deng’s entropy and it can be degenerated to the Deng entropy in the closed world wherever necessary. In order to test the reasonability and effectiveness of the extended belief entropy, an EDEOW-based information fusion approach is proposed and applied to sensor data fusion under uncertainty circumstance. The experimental results verify the usefulness and applicability of the extended measure as well as the modified sensor data fusion method. In addition, a few open issues still exist in the current work: the necessary properties for a belief entropy in the open world assumption, whether there exists a belief entropy that satisfies all the existed properties, and what is the most proper fusion frame for sensor data fusion under uncertainty.

A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks

Measuring centrality has recently attracted increasing attention, with algorithms ranging from those that simply calculate the number of immediate neighbors and the shortest paths to those that are complicated iterative refinement processes and objective dynamical approaches. Indeed, vital nodes identification allows us to understand the roles that different nodes play in the structure of a network. However, quantifying centrality in complex networks with various topological structures is not an easy task. In this paper, we introduce a novel definition of entropy-based centrality, which can be applicable to weighted directed networks. By design, the total power of a node is divided into two parts, including its local power and its indirect power. The local power can be obtained by integrating the structural entropy, which reveals the communication activity and popularity of each node, and the interaction frequency entropy, which indicates its accessibility. In addition, the process of influence propagation can be captured by the two-hop subnetworks, resulting in the indirect power. In order to evaluate the performance of the entropy-based centrality, we use four weighted real-world networks with various instance sizes, degree distributions, and densities. Correspondingly, these networks are adolescent health, Bible, United States (US) airports, and Hep-th, respectively. Extensive analytical results demonstrate that the entropy-based centrality outperforms degree centrality, betweenness centrality, closeness centrality, and the Eigenvector centrality.

The integration of weighted gene association networks based on information entropy

Constructing genome scale weighted gene association networks (WGAN) from multiple data sources is one of research hot spots in systems biology. In this paper, we employ information entropy to describe the uncertain degree of gene-gene links and propose a strategy for data integration of weighted networks. We use this method to integrate four existing human weighted gene association networks and construct a much larger WGAN, which includes richer biology information while still keeps high functional relevance between linked gene pairs. The new WGAN shows satisfactory performance in disease gene prediction, which suggests the reliability of our integration strategy. Compared with existing integration methods, our method takes the advantage of the inherent characteristics of the component networks and pays less attention to the biology background of the data. It can make full use of existing biological networks with low computational effort.

Comparison of ancient and modern Chinese based on complex weighted networks

In this study, we compare statistical properties of ancient and modern Chinese within the framework of weighted complex networks. We examine two language networks based on different Chinese versions of the Records of the Grand Historian. The comparative results show that Zipf's law holds and that both networks are scale-free and disassortative. The interactivity and connectivity of the two networks lead us to expect that the modern Chinese text would have more phrases than the ancient Chinese one. Furthermore, by considering some of the topological and weighted quantities, we find that expressions in ancient Chinese are briefer than in modern Chinese. These observations indicate that the two languages might have different linguistic mechanisms and combinatorial natures, which we attribute to the stylistic differences and evolution of written Chinese.

The network of plants volatile organic compounds

Plants emission of Volatile Organic Compounds (VOCs) is involved in a wide class of ecological functions, as VOCs play a crucial role in plants interactions with biotic and abiotic factors. Accordingly, they vary widely across species and underpin differences in ecological strategy. In this paper, VOCs spontaneously emitted by 109 plant species (belonging to 56 different families) have been qualitatively and quantitatively analysed in order to provide an alternative classification of plants species. In particular, by using bipartite networks methodology from Complex Network Theory, and through the application of community detection algorithms, we show that is possible to classify species according to chemical classes such as terpenes and sulfur compounds. Such complex network analysis allows to uncover hidden plants relationships related to their evolutionary and adaptation to the environment story.

A modified belief entropy in Dempster-Shafer framework

How to quantify the uncertain information in the framework of Dempster-Shafer evidence theory is still an open issue. Quite a few uncertainty measures have been proposed in Dempster-Shafer framework, however, the existing studies mainly focus on the mass function itself, the available information represented by the scale of the frame of discernment (FOD) in the body of evidence is ignored. Without taking full advantage of the information in the body of evidence, the existing methods are somehow not that efficient. In this paper, a modified belief entropy is proposed by considering the scale of FOD and the relative scale of a focal element with respect to FOD. Inspired by Deng entropy, the new belief entropy is consistent with Shannon entropy in the sense of probability consistency. What’s more, with less information loss, the new measure can overcome the shortage of some other uncertainty measures. A few numerical examples and a case study are presented to show the efficiency and superiority of the proposed method.

A Weighted Belief Entropy-Based Uncertainty Measure for Multi-Sensor Data Fusion

In real applications, how to measure the uncertain degree of sensor reports before applying sensor data fusion is a big challenge. In this paper, in the frame of Dempster-Shafer evidence theory, a weighted belief entropy based on Deng entropy is proposed to quantify the uncertainty of uncertain information. The weight of the proposed belief entropy is based on the relative scale of a proposition with regard to the frame of discernment (FOD). Compared with some other uncertainty measures in Dempster-Shafer framework, the new measure focuses on the uncertain information represented by not only the mass function, but also the scale of the FOD, which means less information loss in information processing. After that, a new multi-sensor data fusion approach based on the weighted belief entropy is proposed. The rationality and superiority of the new multi-sensor data fusion method is verified according to an experiment on artificial data and an application on fault diagnosis of a motor rotor.

Defending Against Advanced Persistent Threats Using Game-Theory

Advanced persistent threats (APT) combine a variety of different attack forms ranging from social engineering to technical exploits. The diversity and usual stealthiness of APT turns them into a central problem of contemporary practical system security, since information on attacks, the current system status or the attacker’s incentives is often vague, uncertain and in many cases even unavailable. Game theory is a natural approach to model the conflict between the attacker and the defender, and this work investigates a generalized class of matrix games as a risk mitigation tool for an advanced persistent threat (APT) defense. Unlike standard game and decision theory, our model is tailored to capture and handle the full uncertainty that is immanent to APTs, such as disagreement among qualitative expert risk assessments, unknown adversarial incentives and uncertainty about the current system state (in terms of how deeply the attacker may have penetrated into the system’s protective shells already). Practically, game-theoretic APT models can be derived straightforwardly from topological vulnerability analysis, together with risk assessments as they are done in common risk management standards like the ISO 31000 family. Theoretically, these models come with different properties than classical game theoretic models, whose technical solution presented in this work may be of independent interest.

On the Wiener Polarity Index of Lattice Networks

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics.

An Examination of Not-For-Profit Stakeholder Networks for Relationship Management: A Small-Scale Analysis on Social Media

Using a small-scale descriptive network analysis approach, this study highlights the importance of stakeholder networks for identifying valuable stakeholders and the management of existing stakeholders in the context of mental health not-for-profit services. We extract network data from the social media brand pages of three health service organizations from the U.S., U.K., and Australia, to visually map networks of 579 social media brand pages (represented by nodes), connected by 5,600 edges. This network data is analyzed using a collection of popular graph analysis techniques to assess the differences in the way each of the service organizations manage stakeholder networks. We also compare node meta-information against basic topology measures to emphasize the importance of effectively managing relationships with stakeholders who have large external audiences. Implications and future research directions are also discussed.

Networks of plants: how to measure similarity in vegetable species

Despite the common misconception of nearly static organisms, plants do interact continuously with the environment and with each other. It is fair to assume that during their evolution they developed particular features to overcome similar problems and to exploit possibilities from environment. In this paper we introduce various quantitative measures based on recent advancements in complex network theory that allow to measure the effective similarities of various species. By using this approach on the similarity in fruit-typology ecological traits we obtain a clear plant classification in a way similar to traditional taxonomic classification. This result is not trivial, since a similar analysis done on the basis of diaspore morphological properties do not provide any clear parameter to classify plants species. Complex network theory can then be used in order to determine which feature amongst many can be used to distinguish scope and possibly evolution of plants. Future uses of this approach range from functional classification to quantitative determination of plant communities in nature.

Receiver-Based Ad Hoc On Demand Multipath Routing Protocol for Mobile Ad Hoc Networks

Decreasing the route rediscovery time process in reactive routing protocols is challenging in mobile ad hoc networks. Links between nodes are continuously established and broken because of the characteristics of the network. Finding multiple routes to increase the reliability is also important but requires a fast update, especially in high traffic load and high mobility where paths can be broken as well. The sender node keeps re-establishing path discovery to find new paths, which makes for long time delay. In this paper we propose an improved multipath routing protocol, called Receiver-based ad hoc on demand multipath routing protocol (RB-AOMDV), which takes advantage of the reliability of the state of the art ad hoc on demand multipath distance vector (AOMDV) protocol with less re-established discovery time. The receiver node assumes the role of discovering paths when finding data packets that have not been received after a period of time. Simulation results show the delay and delivery ratio performances are improved compared with AOMDV.

On Hunting Animals of the Biometric Menagerie for Online Signature

Individuals behave differently regarding to biometric authentication systems. This fact was formalized in the literature by the concept of Biometric Menagerie, defining and labeling user groups with animal names in order to reflect their characteristics with respect to biometric systems. This concept was illustrated for face, fingerprint, iris, and speech modalities. The present study extends the Biometric Menagerie to online signatures, by proposing a novel methodology that ties specific quality measures for signatures to categories of the Biometric Menagerie. Such measures are combined for retrieving automatically writer categories of the extended version of the Biometric Menagerie. Performance analysis with different types of classifiers shows the pertinence of our approach on the well-known MCYT-100 database.

Analysis of the Velocity Distribution in Partially-Filled Circular Pipe Employing the Principle of Maximum Entropy

The flow velocity distribution in partially-filled circular pipe was investigated in this paper. The velocity profile is different from full-filled pipe flow, since the flow is driven by gravity, not by pressure. The research findings show that the position of maximum flow is below the water surface, and varies with the water depth. In the region of near tube wall, the fluid velocity is mainly influenced by the friction of the wall and the pipe bottom slope, and the variation of velocity is similar to full-filled pipe. But near the free water surface, the velocity distribution is mainly affected by the contractive tube wall and the secondary flow, and the variation of the velocity is relatively small. Literature retrieval results show relatively less research has been shown on the practical expression to describe the velocity distribution of partially-filled circular pipe. An expression of two-dimensional (2D) velocity distribution in partially-filled circular pipe flow was derived based on the principle of maximum entropy (POME). Different entropies were compared according to fluid knowledge, and non-extensive entropy was chosen. A new cumulative distribution function (CDF) of partially-filled circular pipe velocity in terms of flow depth was hypothesized. Combined with the CDF hypothesis, the 2D velocity distribution was derived, and the position of maximum velocity distribution was analyzed. The experimental results show that the estimated velocity values based on the principle of maximum Tsallis wavelet entropy are in good agreement with measured values.

On Wiener polarity index of bicyclic networks

Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index is also related to the cluster coefficient of networks. In this paper, based on some graph transformations, we determine the sharp upper bound of the Wiener polarity index among all bicyclic networks. These bounds help to understand the underlying quantitative graph measures in depth.

An Extended N-Player Network Game and Simulation of Four Investment Strategies on a Complex Innovation Network

As computer science and complex network theory develop, non-cooperative games and their formation and application on complex networks have been important research topics. In the inter-firm innovation network, it is a typical game behavior for firms to invest in their alliance partners. Accounting for the possibility that firms can be resource constrained, this paper analyzes a coordination game using the Nash bargaining solution as allocation rules between firms in an inter-firm innovation network. We build an extended inter-firm n-player game based on nonidealized conditions, describe four investment strategies and simulate the strategies on an inter-firm innovation network in order to compare their performance. By analyzing the results of our experiments, we find that our proposed greedy strategy is the best-performing in most situations. We hope this study provides a theoretical insight into how firms make investment decisions.

Petri Net and Probabilistic Model Checking Based Approach for the Modelling, Simulation and Verification of Internet Worm Propagation

Internet worms are analogous to biological viruses since they can infect a host and have the ability to propagate through a chosen medium. To prevent the spread of a worm or to grasp how to regulate a prevailing worm, compartmental models are commonly used as a means to examine and understand the patterns and mechanisms of a worm spread. However, one of the greatest challenge is to produce methods to verify and validate the behavioural properties of a compartmental model. This is why in this study we suggest a framework based on Petri Nets and Model Checking through which we can meticulously examine and validate these models. We investigate Susceptible-Exposed-Infectious-Recovered (SEIR) model and propose a new model Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered) (SEIDQR(S/I)) along with hybrid quarantine strategy, which is then constructed and analysed using Stochastic Petri Nets and Continuous Time Markov Chain. The analysis shows that the hybrid quarantine strategy is extremely effective in reducing the risk of propagating the worm. Through Model Checking, we gained insight into the functionality of compartmental models. Model Checking results validate simulation ones well, which fully support the proposed framework.

Hardness Analysis and Empirical Studies of the Relations among Robustness, Topology and Flow in Dynamic Networks

Network robustness is the ability of a network to maintain performance after disruption, thus it is an important index for network designers to refer to. Every actual network has its own topology structure, flow magnitude (scale) and flow distribution. How the robustness relates to these factors still remains unresolved. To analyze the relations, we first established a robustness problem model, studied the hardness of a special case of the model, and generated a lot of representative network instances. We conducted experiments on these instances, deleting 5% to 50% edges on each instance and found that the robustness of a network has an approximate linearity to its structural entropy and flow entropy, when the correlation coefficient between the structure and flow is fixed. We also found that robustness is unlikely to have a relation to the flow scale and edge scale in our model. The empirical studies thus can provide a way of quickly estimating the robustness of real-world networks by using the regression coefficients we obtained during the experiments. We conducted computation on a real-world dataset and got favorable results, which exhibited the effectiveness of the estimation.

Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks

The main finding of this paper is a novel avalanche-size exponent τ ≈ 1.87 when the generalised sandpile dynamics evolves on the real-world Japanese inter-firm network. The topology of this network is non-layered and directed, displaying the typical bow tie structure found in real-world directed networks, with cycles and triangles. We show that one can move from a strictly layered regular lattice to a more fluid structure of the inter-firm network in a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distribution for the interactions, forces the scaling exponent of the avalanche-size probability density function τ out of the two-dimensional directed sandpile universality class τ = 4/3, into the mean field universality class τ = 3/2. Numerical investigation shows that these two classes are the only that exist on the directed sandpile, regardless of the underlying topology, as long as it is strictly layered. Randomly adding a small proportion of links connecting non adjacent layers in an otherwise layered network takes the system out of the mean field regime to produce non-trivial avalanche-size probability density function. Although these do not display proper scaling, they closely reproduce the behaviour observed on the Japanese inter-firm network.

Bayes Node Energy Polynomial Distribution to Improve Routing in Wireless Sensor Network

Wireless Sensor Network monitor and control the physical world via large number of small, low-priced sensor nodes. Existing method on Wireless Sensor Network (WSN) presented sensed data communication through continuous data collection resulting in higher delay and energy consumption. To conquer the routing issue and reduce energy drain rate, Bayes Node Energy and Polynomial Distribution (BNEPD) technique is introduced with energy aware routing in the wireless sensor network. The Bayes Node Energy Distribution initially distributes the sensor nodes that detect an object of similar event (i.e., temperature, pressure, flow) into specific regions with the application of Bayes rule. The object detection of similar events is accomplished based on the bayes probabilities and is sent to the sink node resulting in minimizing the energy consumption. Next, the Polynomial Regression Function is applied to the target object of similar events considered for different sensors are combined. They are based on the minimum and maximum value of object events and are transferred to the sink node. Finally, the Poly Distribute algorithm effectively distributes the sensor nodes. The energy efficient routing path for each sensor nodes are created by data aggregation at the sink based on polynomial regression function which reduces the energy drain rate with minimum communication overhead. Experimental performance is evaluated using Dodgers Loop Sensor Data Set from UCI repository. Simulation results show that the proposed distribution algorithm significantly reduce the node energy drain rate and ensure fairness among different users reducing the communication overhead.

PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks

Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman’s original method which had evidently gone unnoticed since its publication over a decade ago.

SHER: a colored petri net based random mobility model for wireless communications

In wireless network research, simulation is the most imperative technique to investigate the network’s behavior and validation. Wireless networks typically consist of mobile hosts; therefore, the degree of validation is influenced by the underlying mobility model, and synthetic models are implemented in simulators because real life traces are not widely available. In wireless communications, mobility is an integral part while the key role of a mobility model is to mimic the real life traveling patterns to study. The performance of routing protocols and mobility management strategies e.g. paging, registration and handoff is highly dependent to the selected mobility model. In this paper, we devise and evaluate the Show Home and Exclusive Regions (SHER), a novel two-dimensional (2-D) Colored Petri net (CPN) based formal random mobility model, which exhibits sociological behavior of a user. The model captures hotspots where a user frequently visits and spends time. Our solution eliminates six key issues of the random mobility models, i.e., sudden stops, memoryless movements, border effect, temporal dependency of velocity, pause time dependency, and speed decay in a single model. The proposed model is able to predict the future location of a mobile user and ultimately improves the performance of wireless communication networks. The model follows a uniform nodal distribution and is a mini simulator, which exhibits interesting mobility patterns. The model is also helpful to those who are not familiar with the formal modeling, and users can extract meaningful information with a single mouse-click. It is noteworthy that capturing dynamic mobility patterns through CPN is the most challenging and virulent activity of the presented research. Statistical and reachability analysis techniques are presented to elucidate and validate the performance of our proposed mobility model. The state space methods allow us to algorithmically derive the system behavior and rectify the errors of our proposed model.