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Accurate traffic flow forecasting is an important technical measure to alleviate traffic congestion. Since traffic flow has spatial and temporal characteristics, thus the adequate extraction of its spatio-temporal features is an important prerequisite to promote the forecast accuracy of the model. However, a majority of existing traffic flow prediction models cannot sufficiently consider the neighborhood spatio-temporal relationship for the real road network in the modeling process, which makes it difficult to improve the model prediction accuracy. For this reason, this paper takes improved feature enhancement graph convolution (FEGC), gated recurrent unit (GRU), and improved lightweight particle swarm optimization (ILPSO) algorithm as components, respectively, to construct a combinatorial traffic flow prediction model FEGC-GRU-ILPSO (FGI), aiming to achieve accurate forecast for regional traffic flow through fully learning spatio-temporal correlation characteristics. Firstly, considering that most traffic flow modeling methods are ineffective in characterizing the hidden association information within nodes, we propose the method of constructing the virtual space adjacency matrix based on the improved gray relational analysis (IGRA) algorithm, which achieves the effective characterization of road network neighborhood relationship by fusing it with the original adjacency matrix. Then, based on the idea of matrix decomposition, the weight adjacency matrix is further introduced to realize the dynamic capture of time-varying correlation of node graph structure in realistic road networks. Secondly, to address the performance degradation problem caused by feature assimilation in multi-layer graph convolution, an improved feature enhancement graph convolution component is proposed to alleviate the multi-layer graph convolution over-smoothing by enhancing salient features. Finally, considering the convex optimization problem caused by the way the hyperparameters of the model are determined through subjective experience, we propose the ILPSO algorithm to improve the overall prediction performance in an adaptive optimizing method. In this paper, real-world data acquired by the Caltrans Performance Measurement System (PeMS) is used as the object of study. The experimental results demonstrate that the FGI model has better prediction performance than the current mainstream baseline models. • An adaptive weighted adjacency matrix is proposed to learn road network features. • A feature enhancement graph convolution is proposed to reinforce important features. • An improved particle swarm algorithm is proposed to optimize the model parameters. • The feature capture process of feature enhancement graph convolution is visualized. • The proposed model has superior prediction accuracy than the baseline models. [ABSTRACT FROM AUTHOR]

A total of 206 co-occurrence networks of Chinese characters and words are constructed from modern Chinese articles. Spectra of the adjacency matrices especially the largest eigenvalues λ 1 , the second largest eigenvalues, the smallest eigenvalues, the number of different eigenvalues N λ , the spectral distribution, and the spectral density ρ (λ) are computed and studied. Some formulas about the statistical parameters are given by applying multiple linear regression analysis. It is found that not only the growth trends of λ 1 and N λ but also the properties of spectral distributions and ρ (λ) do not change with the network size. Therefore, the spectral behavior of the modern Chinese linguistic topology is consistent over time unless something having a major impact on Chinese language happen. [ABSTRACT FROM AUTHOR]

Abstract This paper adopts network analysis to investigate the feasibility of recruiting nearby fishing vessels as the initial rescue force for search-and-rescue operations. Network analysis was conducted to analyze the proximity among fishing vessels according to the type of fishing. The results were used as input to an adjacency matrix and schematized by applying the network. Given that fish species tend to travel together, fishing vessels in pursuit of them also operate in the same waters, essentially forming a network. It is thus desirable to secure a search-and-rescue system among fishing vessels of the same fishing type for prompt rescue. Specifically, network analysis confirmed that fishing vessels of the same type within 10 nautical miles can become vigilant, and a system of prompt rescue support can thus be secured; this approach improves the overall speed of rescue operations. These findings can be used as baseline data for developing a practical search-and-rescue system through a network of fishing vessels of the same fishing type. Highlights • Network analysis to evaluate the proximity among fishing vessels by fishing type. • Study utilized the fishing vessel location data for a 1 month span. • Intensity of the connection between two vessels by relative weight. • Network analysis can be applied to developing a rescue system. [ABSTRACT FROM AUTHOR]

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in the literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several metrics of the graph. However, it is not always clear whether this representation is unique, as the permutation of rows and columns in the matrix can represent the same graph. To address this issue, the proposed methodology employs a sorting algorithm to rearrange the elements of the adjacency matrix of a complex graph in a specific order. The resulting sorted adjacency matrix is then used as input for feature extraction and machine learning algorithms to classify the networks. The results indicate that the proposed methodology outperforms previous literature results on synthetic and real-world data. • This work presents a new technique for extracting important features of complex networks to improve machine learning performance. • The proposed methodology employs sorting algorithm to rearrange the elements of adjacency matrix of complex graph. • The resulting sorted adjacency matrix is then used as input for feature extraction and machine learning classification. • Results indicate that the proposed methodology outperforms previous literature results in synthetic and real-world data. [ABSTRACT FROM AUTHOR]

Some topological features of recursive trees are quantified by exploiting the decomposition of directed graphs into a suitable combination of starlike hierarchical and three-edge cyclic components. This approach requires the adoption of the formalism of weighted directed graphs and allows us to quantify the proportion of hierarchical and hidden cyclic components. Using this concept, we can introduce new local parameters and global measures that quantify certain topological features of recursive trees. The average values of some of these measures over the general set of same-sized recursive trees are also determined. • Adjacency matrices are built up of orthogonal cyclic and hierarchical components. • This decomposition is applied to recursive trees, revealing hidden cyclic components. • New local and global quantities describing topological features are introduced. • Their ability to separate recursive trees into their isomorphism classes is studied. • The averages of some of them over same-sized recursive trees are exactly determined. [ABSTRACT FROM AUTHOR]

Spectral analysis is a powerful tool that provides global measures of the network properties. In this paper, 200 English articles are collected. A word co-occurrence network is constructed from each single article (denoted by single network). Furthermore, 5 large English word co-occurrence networks are constructed (denoted by large network). Spectra of their adjacency matrices are computed. The largest eigenvalue, λ 1 , depends on the network size N and the number of edges E as λ 1 ∝ N 0.66 and λ 1 ∝ E 0.54 , respectively. The number of different eigenvalues, N λ , increase in the manner of N λ ∝ N 0.58 and N λ ∝ E 0.47 . The middle part of the spectral distribution can be fitted by a line with slope − 0.01 in each of the large networks, whereas two segments with the same slope − 0.03 for 0 ≪ N < 260 and − 0.02 for 260 < N < 2800 are needed for the single networks. An “M”-shape distribution appears in each of the spectral densities of the large networks. These and other results can provide useful insight into the structural properties of English linguistic networks. [ABSTRACT FROM AUTHOR]

The eigenvalues and eigenvectors of the adjacency matrix of a network contain essential information about its topology. For each of the Chinese language co-occurrence networks constructed from four literary genres, i.e., essay, popular science article, news report, and novel, it is found that the largest eigenvalue depends on the network size N , the number of edges, the average shortest path length, and the clustering coefficient. Moreover, it is found that their node-degree distributions all follow a power-law. The number of different eigenvalues, N λ , is found numerically to increase in the manner of N λ ∝ log N for novel and N λ ∝ N for the other three literary genres. An “M” shape or a triangle-like distribution appears in their spectral densities. The eigenvector corresponding to the largest eigenvalue is mostly localized to a node with the largest degree. For the above observed phenomena, mathematical analysis is provided with interpretation from a linguistic perspective. [ABSTRACT FROM AUTHOR]

Research on complex networks is becoming a very hot topic in recent years, among which node matching problem is an important issue. The aim of node matching problem is to find out the corresponding relations between the individuals of associated networks. Traditional node matching problem of networks always hypothesize that a proportion of matching nodes are known. However, if the ratio of matched nodes is very small, the matching accuracy of the remaining nodes cannot be evaluated accurately. What is more, we may have not any matched nodes for reference at all. In view of this, this paper established the mathematic model of node matching problem based on the adjacency matrixes of networks, and presented an evolutionary algorithm to solve it. The experimental results show that the proposed method can achieve satisfactory matching precision in the absence of any matched nodes. [ABSTRACT FROM AUTHOR]

Two novel centrality indices, PathRank and Icentr, are defined. PathRank is a generalization of the PageRank algorithm, suitable to rank nodes of undirected graphs according to number and weight of paths in the graph. Icentr ranks the nodes of the graph by means of a combination of the weights of nodes and edges, scaled according to the distance from each node, one at a time. We apply the two novel indices to underground transportation networks, since these networks represent an infrastructural backbone for the transportation system of most big cities over the world. The characterization of the most important components of those networks and the simulation of their responses when they stop working properly, are vital for maintaining the mobility service at a desirable level. Since there are different ways to associate a graph to an underground network according to the degree of detail and aims of the study, we describe the methodology we adopted to associate a graph to such a network. The methodology was applied to 34 underground networks of worldwide cities, and the resulting graphs constitute the reference dataset. A detailed study of both Boston network and the dataset is proposed as prototypal for either a graph alone or all graphs in a dataset. Results show how different features of graphs are revealed by the two novel indices. [ABSTRACT FROM AUTHOR]

Abstract: Since the last decade, minimal spanning trees (MSTs) have become one of the main streams in econophysics to filter the important information contained, for example, in stock networks. The standard practice to find an MST is by using Kruskal’s algorithm. However, it becomes slower and slower when the number of stocks gets larger and larger. In this paper we propose an algorithm to find an MST which has considerably promising performance. It is significantly faster than Kruskal’s algorithm and far faster if there is only one unique MST in the network. Our approach is based on the combination of fuzzy relation theory and graph theoretical properties of the forest of all MSTs. A comparison study based on real data from four stock markets and four types of simulated data will be presented to illustrate the significant advantages of the proposed algorithm. [Copyright &y& Elsevier]

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population (Yengo et al., 2019). This result brings our attention again to a math problem related to inbreeding family trees and diversity. Groups with a finite number of individuals could give a variety of genetic relationships. In previous works (Caruso and Jarne, 2015; Caruso and Jarne, 2014; Jarne and Caruso, 2019), we have addressed the issue of building inbreeding trees for biparental reproduction using Markovian models. Here, we extend these studies by presenting an algorithm to generate and represent inbreeding trees with no overlapping generations. We explicitly assume a two-gender reproductory scheme, and we pay particular attention to the links between nodes. We show that even for a simple case with a relatively small number of nodes in the tree, there are a large number of possible ways to rearrange the links between generations. We present an open-source python code to generate the tree graph, the adjacency matrix, and the histogram of the links for each different tree representation. We show how this mapping reflects the difference between tree realizations, and how valuable information may be extracted upon inspection of these matrices. The algorithm includes a feature to average several tree realizations, obtain the connectivity distribution, and calculate the mean value and standard deviation. We used this feature to compare trees with a different number of generations and nodes. The code presented here, available in Git-Hub, may be easily modified to be applied to other areas of interest involving connections between individuals, extend the study to add more characteristics of the different nodes, etc. • We describe a model and give a set of rules to construct a tree of ancestors. • We present an algorithm and an open code to produce different tree realizations. • We show a way of visualizing inbreeding trees with adjacency matrices and histograms. • It is possible to average tree realizations and obtain the output link distribution. [ABSTRACT FROM AUTHOR]

The spectrum of a network provides important information about its global structure. For Chinese character co-occurrence networks constructed from articles published in 11 different historical periods in China, the spectra and eigenvectors of their adjacency matrices are studied. It is found that the middle part of the spectral distribution can be fitted by a line with slope − 0. 01 in each incorporated network, whereas two segments with the same slope − 0. 02 are needed for other single networks. If the eigenvalues, λ i , are listed in decreasing order, then the formers depend on their ranks, i , in the form of λ i ∝ − β log i , where 1. 70 ≤ β ≤ 9. 69. In the spectral density ρ (λ) , there is a triangle-like shape in each of the incorporated networks, while the ρ (λ) values are nearly symmetrical in each single network. These and other results indicate that the spectra and eigenvectors can provide useful insight into the structural properties of Chinese linguistic networks. • A total of 561 Chinese character co-occurrence networks' spectra are computed. • The largest eigenvalue depends on N, E, L, and C as scale free, respectively. • The number of different eigenvalues grows linearly with N. • The single network's spectral distribution can be fitted by two segments with the same slope -0.02. • A triangle shape appears in each of the large networks' spectral densities. [ABSTRACT FROM AUTHOR]

Community structure is widespread in the form of complex networks and is important. However, research on detecting community structure (community detection) still has some unsolved problems. In this paper, we introduce a new community detection algorithm, called Commansor (Com munity Detection Based on Hu man So cial Behavi or), which automatically detects communities in the network by simulating human social behavior. The fundamental principle of Commansor is finding the social comfort zone of human beings in the social process and simulating the evolution of social network structure in the information spreading process. Different closeness relationships between nodes form a comfort zone for each node, and the process of information spreading has an important impact on the evolution of the community structure. The main steps of the Commansor algorithm include (a) finding a comfort zone for each node by using closeness matrices , (b) randomly selecting an associated node from the comfort zone for each node to reconstruct a simplified network, and (c) adjusting the simplified network structure by simulating the process of information spreading in human society. We compared Commansor with a range of typical algorithms by performing extensive experiments on synthetic networks and real-world networks. The experiments proved that, in most cases, our algorithm is superior to the compared algorithms in terms of the quality of community detection. • A new perspective on community detection : We discover communities by simulating human social behavior. And some new theory has been proposed. • Higher accuracy : A large number of experiments have proved that the community detection accuracy of our algorithm is the highest in most cases. • Parameter-free : Commansor does not require parameter settings, and does not rely on prior knowledge. • Universality : It has been proven by a series of experiments that our algorithm performs well on networks that differ in scale, complexity, and community size. [ABSTRACT FROM AUTHOR]