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The study of citation networks is of interest to the scientific community. However, the underlying mechanism driving individual citation behavior remains imperfectly understood, despite the recent proliferation of quantitative research methods. Traditional network models normally use graph theory to consider articles as nodes and citations as pairwise relationships between them. In this paper, we propose an alternative evolutionary model based on hypergraph theory in which one hyperedge can have an arbitrary number of nodes, combined with an aging effect to reflect the temporal dynamics of scientific citation behavior. Both theoretical approximate solution and simulation analysis of the model are developed and validated using two benchmark datasets from different disciplines, i.e. publications of the American Physical Society (APS) and the Digital Bibliography & Library Project (DBLP). Further analysis indicates that the attraction of early publications will decay exponentially. Moreover, the experimental results show that the aging effect indeed has a significant influence on the description of collective citation patterns. Shedding light on the complex dynamics driving these mechanisms facilitates the understanding of the laws governing scientific evolution and the quantitative evaluation of scientific outputs.

Vertices in the same group tend to connect densely, and usually share common attributes. Groups of different sizes reflect the relations of vertices in different ranges, and also reflect the features of different orders of the network. In this work, we propose a novel network representation learning algorithm by introducing group features of vertices of different orders to learn more discriminative network representations, named as network representation learning algorithm using Hierarchical structure embedding (HSNR). HSNR algorithm firstly constructs hierarchical relations of network structures of different orders based on greedy algorithm and modularity. In order to introduce hierarchical features into the network representation learning model, HSNR algorithm then introduces the idea of multi-relational modeling from knowledge representation, and converts the hierarchical relations into the triplet form between vertices. Finally, HSNR proposes a joint learning model embedding vertex triplets into the network representations. The experimental results show that the HSRN algorithm presented has an excellent performance in network vertex classification task on three real-world datasets.

The nodes in interdependent network have both information exchange and information dissemination, and the node degree correlation of network is easier to divide into different community structures. In order to study invulnerability of such networks, the global topology and the local community properties of network are considered in this paper, and attack strategies are proposed based on node overlapping degree and community structure. The relative size $s$ of the most connected sub-graph and global efficiency $E$ of the network are taken as invulnerability measures. Firstly, two kinds of interdependent network models are constructed by using correlation of nodes in different levels (random correlation and preferential correlation), and their static topological indexes are analyzed. Secondly, invulnerability experiments are carried with two kinds of synthetic networks in different attack strategies. Finally, as the application of model, the “aviation-information” empirical network is constructed, and the influence of information network topology on the aviation network is explored. Combined with numerical simulation, attack strategy based on community structure is the most effective. The network generated by random correlation mechanism between layers has better invulnerability. Small-world information network has little influence on the invulnerability of aviation information network. The results of this paper have a certain guiding significance for model construction mechanism of the invulnerability of interdependent networks.

Network representation learning plays an important role in the field of network data mining. By embedding network structures and other features into the representation vector space of low dimensions, network representation learning algorithms can provide high-quality feature input for subsequent tasks, such as network link prediction, network vertex classification, and network visualization. The existing network representation learning algorithms can be trained based on the structural features, vertex texts, vertex tags, community information, etc. However, there exists a lack of algorithm of using the future evolution results of the networks to guide the network representation learning. Therefore, this paper aims at modeling the future network evolution results of the networks based on the link prediction algorithm, introducing the future link probabilities between vertices without edges into the network representation learning tasks. In order to make the network representation vectors contain more feature factors, the text features of the vertices are also embedded into the network representation vectors. Based on the above two optimization approaches, we propose a novel network representation learning algorithm, Network Representation learning algorithm based on the joint optimization of Three Features (TFNR). Based on Inductive Matrix Completion (IMC), TFNR algorithm introduces the future probabilities between vertices without edges and text features into the procedure of modeling network structures, which can avoid the problem of the network structure sparse. Experimental results show that the proposed TFNR algorithm performs well in network vertex classification and visualization tasks on three real citation network datasets.

Let us model the network by an undirected graph G, in which each edge fails independently with probability q ∈ [ 0 , 1 ] , the all-terminal reliability of the network is the probability that the graph G remains connected and it is one of the important measure for the invulnerability of the network. Clearly, the all-terminal reliability can be written as a polynomial in either q. Theoretically, it has been proved that calculating all-terminal reliability for planar networks is #P-complete. Up now we cannot find any results for some special classes of the planar networks. This paper studies the all-terminal reliability of the two-tree networks and its generalizations. A linear algorithm for calculating the reliability of a planar two-tree networks is proposed, with algorithmic complexity O ( n ) , where n is the number of steps. Then both the uniformly-most reliable network model and the uniformly-worst reliable network model are determined by using the algorithm. Finally, a polynomial algorithm for planar two-connected networks is proposed based on an expended algorithm and the corresponding uniformly-most reliable network model and uniformly-worst reliable network model are also presented, with computational complexity O ( n ) , where n is the number of steps.

Network reliability plays an important role in analysis, synthesis and detection of real-world networks. In this paper, we first propose the concept of hypernetwork reliability, which generalizes the concept of network reliability. The model for hypernetwork reliability studies consists of a hypergraph with perfect reliable vertices and equal and independent hyperedge failure probability [Formula: see text]. The measure of reliability is defined as the probability that a hypergraph is connected. Let [Formula: see text] be an [Formula: see text]-uniform hypergraph with the number of vertices [Formula: see text] and the number of hyperedges [Formula: see text], where every hyperedge connects [Formula: see text] vertices. We confirm the possibility of the existence of a fixed hypergraph that is optimal or least for all hyperedges same survival possible [Formula: see text]. It is simple to verify that such hypergraph exists if [Formula: see text]. For a kind of 2-regular 3-uniform hypergraphs, we calculate the upper and lower bounds on the all-terminal reliability, and describe the class of hypergraphs that reach the boundary.

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.

The evolution of hypernetworks is mostly based on growth and preferential connection. During the construction process, the number of new nodes and hyperedges is increasing infinitely. However, in the network, considering the impact of real resources and environment, the nodes can not grow without the upper limit, and the number of connections can not grow without the upper limit. Under certain conditions, there will be the optimal or maximum growth number. In addition, with the increase of the size of the hypernetwork and the number of nodes, there will be more old nodes waiting to be selected. Based on the problems in the process of constructing the hypernetwork, this paper improves the construction of the hypernetwork, and proposes a hypernetwork model construction method based on logical regression. Firstly, the maximum growth number of nodes is set to limit its growth, and the maximum capacity is set for each hyperedge; Secondly, the connection between nodes is selected by using logical regression instead of preferential connection; Finally, the old nodes are selected by using sub linear growth function instead of constant. Through the simulation experiment, it is found that the hyperdegree distribution of the improved hypernetwork model conforms to the power-law distribution; by changing the network scale, hyperedge capacity, the number of new nodes added and the number of old nodes selected in the process of the construction of the hypernetwork, the change law of the hypernetwork model's hyperdegree distribution is studied.

A graph G with k specified target vertices in vertex set is a k -terminal graph. The k -terminal reliability is the connection probability of the fixed k target vertices in a k -terminal graph when every edge of this graph survives independently with probability p . For the class of two-terminal graphs with a large number of edges, Betrand, Goff, Graves, and Sun constructed a locally most reliable two-terminal graph for p close to 1 and illustrated by a counterexample that this locally most reliable graph is not the uniformly most reliable two-terminal graph. At the same time, they also determined that there is a uniformly most reliable two-terminal graph in the class obtained by deleting an edge from the complete graph with two target vertices. This article focuses on the uniformly most reliable three-terminal graph of dense graphs with n vertices and m edges. First, we give the locally most reliable three-terminal graphs of n and m in certain ranges for p close to 0 and 1. Then, it is proved that there is no uniformly most reliable three-terminal graph with specific n and m , where n ≥ 7 and n 2 − ⌊ n − 3 / 2 ⌋ ≤ m ≤ n 2 − 2 . Finally, some uniformly most reliable graphs are given for n vertices and m edges, where 4 ≤ n ≤ 6 and m = n 2 − 2 or n ≥ 5 and m = n 2 − 1 .

Network representation learning called NRL for short aims at embedding various networks into low-dimensional continuous distributed vector spaces. Most existing representation learning methods focus on learning representations purely based on the network topology, i.e., the linkage relationships between network nodes, but the nodes in lots of networks may contain rich text features, which are beneficial to network analysis tasks, such as node classification, link prediction and so on. In this paper, we propose a novel network representation learning model, which is named as Text-Enhanced Network Representation Learning called TENR for short, by introducing text features of the nodes to learn more discriminative network representations, which come from joint learning of both the network topology and text features, and include common influencing factors of both parties. In the experiments, we evaluate our proposed method and other baseline methods on the task of node classification. The experimental results demonstrate that our method outperforms other baseline methods on three real-world datasets.

Cascading failures are widely found in hyper-networks. In this paper, a new cascading failure model based on couple map lattice is proposed in terms of the hyper-adjacent matrix and joint degree. The cascading failure model is rather universal describing the cascading failure behavior of k uniform hyper-network and many typical complex networks. Simulation results show that 3 uniform scale-free hyper-network is robust against random attacks but is vulnerable to deliberate attacks. In addition, a scale-free hyper-network is more robust than a general complex network against the same attack. Finally, an approximate solution to the disturbance threshold of k uniform scale-free hyper-network is obtained.

At present, most link prediction algorithms only consider the connection between nodes and nodes, which is one-to-one, and it does not consider the contribution to the neighbor nodes of the nodes to the prediction performance of the target nodes, having poor prediction performance on sparse networks. To solve this problem, a link prediction algorithm based on the gravitational field of complex network is proposed in this paper. Firstly, the nodes in the complex network are abstracted into the mass points in the Gravitation field, and the complex network gravitational field model is established from the point of view of physics. Secondly, the direct gravitational value between two nodes is calculated by using the complex network gravitational field model, and then the indirect gravitational values of the first order neighbors of the target nodes between two nodes are calculated. After that, summed the direct gravitational values with the indirect gravitational values as the similarity value between the two nodes. Finally, the gravitational similarity matrix is constructed and the gravitational similarity matrix is normalized. In this paper, a large number of experiments are carried out on four real datasets. The Experiments results show that, compared with the traditional link prediction algorithms, the prediction performance of most traditional link prediction algorithms has been improved to a certain extent by using the presented method to optimize various traditional link prediction algorithms, and the validity and feasibility of link prediction algorithm based on the gravitational field of complex network are affirmed.

Network representation learning is a key research field in network data mining. In this paper, we propose a novel multi-view network representation algorithm (MVNR), which embeds multi-scale relations of network vertices into the low dimensional representation space. In contrast to existing approaches, MVNR explicitly encodes higher order information using k-step networks. In addition, we introduce the matrix forest index as a kind of network feature, which can be applied to balance the representation weights of different network views. We also research the relevance amongst MVNR and several excellent research achievements, including DeepWalk, node2vec and GraRep and so forth. We conduct our experiment on several real-world citation datasets and demonstrate that MVNR outperforms some new approaches using neural matrix factorization. Specifically, we demonstrate the efficiency of MVNR on network classification, visualization and link prediction tasks.

Network representation learning based on neural network originates from language modeling based on neural network. These two types of tasks are then studied and applied along different paths. DeepWalk is the most classical network representation learning algorithm, which samples the next hop nodes of the walker with an equal probability method through the random walk strategy. Node2vec improves the random walk procedures, thus improving the performance of node2vec algorithm on various tasks. Therefore, we propose an improved DeepWalk algorithm based on preference random walk (PDW), which modifies the single undirected edge into two one-way directed edges in the network, and then gives each one-way directed edge a walk probability based on local random walk algorithm. In the procedures of acquiring walk sequences, the walk probability of the paths that have been walked will be attenuated according to the attenuation coefficient. For the last hop node of the current node in the walk sequences, an inhibition coefficient is set to prevent random walker from returning to the last node with a greater probability. In addition, we introduce the Alias sampling method in order to obtain the next hop node from the neighboring nodes of current node with a non-equal probability sampling. The experimental results show that the proposed PDW algorithm possesses a stable performance of network representation learning, the network node classification performance is better than that of the baseline algorithms used in this paper.

Hypernetworks can be used to represent information networks, such as computer systems and wireless communication networks, which have higher requirements for reliability. In this paper, a concept of reliability to measure the possibility for the hypernetwork to connect when hyperedge may fail is proposed. A greedy algorithm for calculating reliability is given. The application of the reliability to the study of two real-world complex systems has shown that these systems can be optimized by simple methods.

Network representation learning (NRL) aims at building a low-dimensional vector for each vertex in a network, which is also increasingly recognized as an important aspect for network analysis. Some current NRL methods only focus on learning representations using the network structure. However, vertices in lots of networks may contain community information or text contents, which could be good for relevant evaluation tasks, such as vertex classification, link prediction and so on. Since it has been proved that DeepWalk is actually equivalent to matrix factorization, we propose community and text-enhanced DeepWalk (CTDW) based on the inductive matrix completion algorithm, which incorporates community features and text features of vertices into NRL under the framework of matrix factorization. In experiments, we evaluate the proposed CTDW compared with other state-of-the-art methods on vertex classification. The experimental results demonstrate that CTDW outperforms other baseline methods on three real-world datasets.

Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

Representation learning aims to encode the relationships of research objects into low-dimensional, compressible, and distributed representation vectors. The purpose of network representation learning is to learn the structural relationships between network vertices. Knowledge representation learning is oriented to model the entities and relationships in knowledge bases. In this paper, we first introduce the idea of knowledge representation learning into network representation learning, namely, we propose a new approach to model the vertex triplet relationships based on DeepWalk without TransE. Consequently, we propose an optimized network representation learning algorithm using multi-relational data, MRNR, which introduces the multi-relational data between vertices into the procedures of network representation learning. Importantly, we adopted a kind of higher order transformation strategy to optimize the learnt network representation vectors. The purpose of MRNR is that multi-relational data (triplets) can effectively guide and constrain the procedures of network representation learning. The experimental results demonstrate that the proposed MRNR can learn the discriminative network representations, which show better performance on network classification, visualization, and case study tasks compared to the proposed baseline algorithms in this paper.

Many hypernetworks in the real world, such as scientific collaboration hypernetworks, actor collaboration hypernetworks, World Wide Web (WWW) and citation hypernetworks, have two evolving mechanisms in their hyperedge growth and preferential attachment. Based on this observation, in this paper we construct a new evolving hypernetwork model. We introduced some basic topological properties, such as node degrees, node hyperdegrees, and hyperedge degrees. After presenting the construction of the evolving hypernetwork model, we focus on the theoretical analysis of the hyperdegrees distribution. We furthermore give numerically simulation this quantity in the limit of large hypernetwork size and find that the new hypernetwork model possesses similar qualitative features with the majority of complex networks that have been previously studied, especially the scale-free property of the hyperdegrees distri-bution.

In the wireless sensor networks (WSNs), the battery energy of sensor node is very limited. So, how to use energy of sensor node effectively to prolong the lifetime of WSNs is a challenge. Now, we mostly adopt the routing algorithm is based on clustering, the drawback of this algorithm is rate of utilization of cluster-head node energy is very high and the network lifetime rapidly shorter. This paper puts forward a kind of routing algorithm in WSNs, it is Distributed Energy Balancing Routing algorithm (DEBR), this algorithm through energy costs (EC) control the rate of utilization of each sensor node in WSNs, thus dump energy of each sensor node is balance and prolong the lifetime of wireless sensor networks.

With the application of satellite navigation becoming more and more widely, increasingly complex electromagnetic environment needs to be dealt with. The anti-jamming capabilities of satellite navigation receivers have got more and more attention, whether in the field of military or civilian. The most important and most widely used class of anti-jamming technology is pre-correlation anti-jamming mean. However, the upper bound of overall anti-jamming capability is less studied when the anti-jamming filter inserted into a digital satellite receiver. In this paper the upper bound of anti-jamming capability for pre-correlation anti-jamming receivers is studied. First of all, the quantization loss is theoretically derived, when the input interference is a continuous wave (CWI). A near-optimal quantization interval criterion is proposed through analyzing the minimize quantization loss. Also, according to the calculation of signal-to-noise ratio (SNR) chain in the receiver, the maximum anti-jamming capability is obtained under the constraint of specified quantization bits and quantization interval. The analysis of the upper bound of anti-jamming capability is very important for the design of anti-jamming receivers, and also improves the anti-jamming theory for all spread spectrum signal receivers.