Analysis and evaluation of the entropy indices of a static network structure

Exploring the Entropy Complex Networks with Latent Interaction

In the present work, we study the introduction of a latent interaction index, examining its impact on the formation and development of complex networks. This index takes into account both observed and unobserved heterogeneity per node in order to overcome the limitations of traditional compositional similarity indices, particularly when dealing with large networks comprising numerous nodes. In this way, it effectively captures specific information about participating nodes while mitigating estimation problems based on network structures. Furthermore, we develop a Shannon-type entropy function to characterize the density of networks and establish optimal bounds for this estimation by leveraging the network topology. Additionally, we demonstrate some asymptotic properties of pointwise estimation using this function. Through this approach, we analyze the compositional structural dynamics, providing valuable insights into the complex interactions within the network. Our proposed method offers a promising tool for studying and understanding the intricate relationships within complex networks and their implications under parameter specification. We perform simulations and comparisons with the formation of Erdös-Rényi and Barabási-Alber-type networks and Erdös-Rényi and Shannon-type entropy. Finally, we apply our models to the detection of microbial communities.

Estimation of Discriminative Multimodal Brain Network Connectivity Using Message-Passing-Based Nonlinear Network Fusion

Effective estimation of brain network connectivity enables better unraveling of the extraordinary complexity interactions of brain regions and helps in auxiliary diagnosis of psychiatric disorders. Considering different modalities can provide comprehensive characterizations of brain connectivity, we propose the message-passing-based nonlinear network fusion (MP-NNF) algorithm to estimate multimodal brain network connectivity. In the proposed method, the initial functional and structural networks were computed from fMRI and DTI separately. Then, we update every unimodal network iteratively, making it more similar to the others in every iteration, and finally converge to one unified network. The estimated brain connectivities integrate complementary information from multiple modalities while preserving their original structure, by adding the strong connectivities present in unimodal brain networks and eliminating the weak connectivities. The effectiveness of the method was evaluated by applying the learned brain connectivity for the classification of major depressive disorder (MDD). Specifically, 82.18% classification accuracy was achieved even with the simple feature selection and classification pipeline, which significantly outperforms the competing methods. Exploration of brain connectivity contributed to MDD identification suggests that the proposed method not only improves the classification performance but also was sensitive to critical disease-related neuroimaging biomarkers.

Habitat suitability modeling of Descurainia sophia medicinal plant using three bivariate models

Climate change has caused medicinal plants to become increasingly endangered. Descurainia sophia (flixweed) is at risk of extinction in Fars Province, Iran, due to climate change and modifications of land use. Flixweed is highly valuable because of its medicinal properties. The conservation of this species using habitat suitability modeling seems necessary. In this research, the geographical locations of D. sophia's distribution in southern Iran were recorded and mapped using ArcGIS 10.2.2. Then, ten important variables affecting the growth of D. sophia medicinal plants were identified and prepared as thematic layers. These variables were, namely, "elevation," "slope degree," "slope aspect," "soil physical characteristics (sand, silt, and clay percentage)," "soil chemical properties (EC and pH)," "annual mean rainfall," "annual mean temperature," "distance to roads," "distance to rivers," and "plan curvature." In this study, three bivariate models, including the "index-of-entropy (IofE)," "frequency ratio (FR)," and "weight of evidence (WofE)," were used for mapping the habitat suitability of D. sophia. Moreover, the ROC curve and AUC index were used for evaluating the accuracy of the models. Based on the results, the IofE model ("AUC": 0.93) was the most accurate, while the FR ("AUC": 0.92) and WofE ("AUC": 0.90) models ranked second and third, respectively. The models in this study can be applied as tools for the protection of endangered medicinal plants. Furthermore, the map could assist planners, decision-makers, and engineers in extending study areas. By determining the habitat maps of medicinal plants, their extinction can be prevented. Such maps can also assist in the propagation of medicinal plants.

Identification of Network Topology Variations Based on Spectral Entropy

Based on the fact that the traditional probability distribution entropy describing a local feature of the system cannot effectively capture the global topology variations of the network, some indicators constructed by the network adjacency matrix and Laplacian matrix come into being. Specifically, these measures are based on the eigenvalues of the scaled Laplace matrix, the eigenvalues of the network communicability matrix, and the spectral entropy based on information diffusion that has been proposed recently, respectively. In this article, we systematically study the dependence of these measures on the topological structure of the network. We prove from various aspects that spectral entropy has a better ability to identify the global topology than the traditional distribution entropy. Furthermore, the indicator based on the eigenvalues of the network communicability matrix achieves good results in some aspects while, overall, the spectral entropy is able to identify network topology variations from a global perspective.

A Network Structure Entropy Considering Series-Parallel Structures

Entropy is an important indicator to measure network heterogeneity. We propose a new network structure entropy, SP (series-parallel) structure entropy, based on the global network topology while adding a medial measure that considers the series-parallel structure. First, the results of special networks show that SP structure entropy can overcome other structure’s entropy deficiencies to some extent. Then, through simulation analysis of typical networks, the validity and applicability of SP structure entropy in describing general networks are verified. Finally, we analyze an enterprise consulting network to demonstrate the superiority of the SP structure entropy for real network analysis.

A Survey of Information Entropy Metrics for Complex Networks

Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts.

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific state space growth rate function.

Stock Net Entropy: Evidence from the Chinese Growth Enterprise Market

By introducing net entropy into a stock network, this paper focuses on investigating the impact of network entropy on market returns and trading in the Chinese Growth Enterprise Market (GEM). In this paper, indices of Wu structure entropy (WSE) and SD structure entropy (SDSE) are considered as indicators of network heterogeneity to present market diversification. A series of dynamic financial networks consisting of 1066 daily nets is constructed by applying the dynamic conditional correlation multivariate GARCH (DCC-MV-GARCH) model with a threshold adjustment. Then, we evaluate the quantitative relationships between network entropy indices and market trading-variables and their bilateral information spillover effects by applying the bivariate EGARCH model. There are two main findings in the paper. Firstly, the evidence significantly ensures that both market returns and trading volumes associate negatively with the network entropy indices, which indicates that stock heterogeneity, which is negative with the value of network entropy indices by definition, can help to improve market returns and increase market trading volumes. Secondly, results show significant information transmission between the indicators of network entropy and stock market trading variables.

Growth dynamics and complexity of national economies in the global trade network

We explore the quantitative nexus among economic growth of a country, diversity and specialization of its productions, and evolution in time of its basket of exports. To this purpose we set up a dynamic model and construct economic complexity measures based on panel data concerning up to 1238 exports of 223 countries for 21 years. Key statistical features pertaining to the distribution of resources in the different exports of each country reveal essential in both cases. The parameters entering the evolution model, combined with counterfactual analyses of synthetic simulations, give novel insight into cooperative effects among different productions and prospects of growth of each economy. The complexity features emerging from the analysis of dynamics are usefully compared with gross domestic product per capita (GDP_pc) and with an original measure of the efficiency of the economic systems. This measure, whose construction starts from an estimate of bare diversity in terms of Shannon's entropy function, is made fully consistent with the degree of specialization of the products. Comparisons of this measure with the model parameters allow clear distinctions, from multiple perspectives, among developed, emerging, underdeveloped and risky economies.