scholarly journals Network entropy using edge-based information functionals

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Furqan Aziz ◽  
Edwin R Hancock ◽  
Richard C Wilson
Keyword(s):  
Diffusion Process ◽  
Complex Networks ◽  
Structural Information ◽  
Structural Complexity ◽  
Network Models ◽  
Quantum Graph ◽  
Heat Diffusion ◽  
Graph Representation ◽  
Edge Based ◽  
Local Edge

Abstract In this article, we present a novel approach to analyse the structure of complex networks represented by a quantum graph. A quantum graph is a metric graph with a differential operator (including the edge-based Laplacian) acting on functions defined on the edges of the graph. Every edge of the graph has a length interval assigned to it. The structural information contents are measured using graph entropy which has been proved useful to analyse and compare the structure of complex networks. Our definition of graph entropy is based on local edge functionals. These edge functionals are obtained by a diffusion process defined using the edge-based Laplacian of the graph using the quantum graph representation. We first present the general framework to define graph entropy using heat diffusion process and discuss some of its properties for different types of network models. Second, we propose a novel signature to gauge the structural complexity of the network and apply the proposed method to different datasets.

scholarly journals Modelling community structure and temporal spreading on complex networks

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Vesa Kuikka
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Community Detection ◽  
Network Structure ◽  
Network Connectivity ◽  
Network Models ◽  
Building Blocks ◽  
Detection Algorithm ◽  
Research Area ◽  
Detection Methods

AbstractWe present methods for analysing hierarchical and overlapping community structure and spreading phenomena on complex networks. Different models can be developed for describing static connectivity or dynamical processes on a network topology. In this study, classical network connectivity and influence spreading models are used as examples for network models. Analysis of results is based on a probability matrix describing interactions between all pairs of nodes in the network. One popular research area has been detecting communities and their structure in complex networks. The community detection method of this study is based on optimising a quality function calculated from the probability matrix. The same method is proposed for detecting underlying groups of nodes that are building blocks of different sub-communities in the network structure. We present different quantitative measures for comparing and ranking solutions of the community detection algorithm. These measures describe properties of sub-communities: strength of a community, probability of formation and robustness of composition. The main contribution of this study is proposing a common methodology for analysing network structure and dynamics on complex networks. We illustrate the community detection methods with two small network topologies. In the case of network spreading models, time development of spreading in the network can be studied. Two different temporal spreading distributions demonstrate the methods with three real-world social networks of different sizes. The Poisson distribution describes a random response time and the e-mail forwarding distribution describes a process of receiving and forwarding messages.

scholarly journals A Novel Method to Predict Drug-Target Interactions Based on Large-Scale Graph Representation Learning

Cancers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 2111
Author(s):  
Bo-Wei Zhao ◽  
Zhu-Hong You ◽  
Lun Hu ◽  
Zhen-Hao Guo ◽  
Lei Wang ◽  
...  
Keyword(s):  
Drug Target ◽  
Large Scale ◽  
Computational Models ◽  
Structural Information ◽  
Characteristic Curve ◽  
Representation Learning ◽  
Graph Representation ◽  
Convolutional Network ◽  
Novel Method

Identification of drug-target interactions (DTIs) is a significant step in the drug discovery or repositioning process. Compared with the time-consuming and labor-intensive in vivo experimental methods, the computational models can provide high-quality DTI candidates in an instant. In this study, we propose a novel method called LGDTI to predict DTIs based on large-scale graph representation learning. LGDTI can capture the local and global structural information of the graph. Specifically, the first-order neighbor information of nodes can be aggregated by the graph convolutional network (GCN); on the other hand, the high-order neighbor information of nodes can be learned by the graph embedding method called DeepWalk. Finally, the two kinds of feature are fed into the random forest classifier to train and predict potential DTIs. The results show that our method obtained area under the receiver operating characteristic curve (AUROC) of 0.9455 and area under the precision-recall curve (AUPR) of 0.9491 under 5-fold cross-validation. Moreover, we compare the presented method with some existing state-of-the-art methods. These results imply that LGDTI can efficiently and robustly capture undiscovered DTIs. Moreover, the proposed model is expected to bring new inspiration and provide novel perspectives to relevant researchers.

scholarly journals Edge-based formulation of elastic network models

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Maxwell Hodges ◽  
Sophia N. Yaliraki ◽  
Mauricio Barahona
Keyword(s):  
Network Models ◽  
Elastic Network ◽  
Elastic Network Models ◽  
Edge Based

scholarly journals Graph fractal dimension and the structure of fractal networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Pavel Skums ◽  
Leonid Bunimovich
Keyword(s):  
Complex Networks ◽  
Evolutionary Biology ◽  
Real Life ◽  
Fractal Dimensions ◽  
Network Models ◽  
Self Similarity ◽  
Descriptive Complexity ◽  
Network Communities ◽  
Fractal Properties ◽  
Continuous Objects

Abstract Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

scholarly journals The Principle of Maximal Simplicity for Modular Inorganic Crystal Structures

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1472
Author(s):  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structures ◽  
Structure Prediction ◽  
Structural Information ◽  
Structural Complexity ◽  
Configurational Entropy ◽  
Sensu Stricto ◽  
Least Action ◽  
Inorganic Crystal ◽  
Principle Of Least Action ◽  
Structure Description

Modularity is an important construction principle of many inorganic crystal structures that has been used for the analysis of structural relations, classification, structure description and structure prediction. The principle of maximal simplicity for modular inorganic crystal structures can be formulated as follows: in a modular series of inorganic crystal structures, the most common and abundant in nature and experiments are those arrangements that possess maximal simplicity and minimal structural information. The latter can be quantitatively estimated using information-based structural complexity parameters. The principle is applied for the modular series based upon 0D (lovozerite family), 1D (biopyriboles) and 2D (spinelloids and kurchatovite family) modules. This principle is empirical and is valid for those cases only, where there are no factors that may lead to the destabilization of simplest structural arrangements. The physical basis of the principle is in the relations between structural complexity and configurational entropy sensu stricto (which should be distinguished from the entropy of mixing). It can also be seen as an analogy of the principle of least action in physics.

IR-laser-induced reflection and conductance wave unlike heat diffusion process in HT SC ceramics

1993 ◽  
Author(s):  
Eugene M. Kudriavtsev ◽  
Yu. I. Rybalko ◽  
Sergey D. Zotov ◽  
Michel L. Autric ◽  
Georges Inglesakis
Keyword(s):  
Diffusion Process ◽  
Heat Diffusion ◽  
Ir Laser

Modern Diffusion of Products with Complex Network Models

2011 ◽  
pp. 119-133
Author(s):  
Atsushi Tanaka
Keyword(s):  
Complex Networks ◽  
Marketing Strategy ◽  
Complex Network ◽  
Network Models ◽  
Information Propagation ◽  
Multiagent Simulation ◽  
Product Marketing ◽  
Winner Takes All ◽  
Complex Network Models

In this chapter, some important matters of complex networks and their models are reviewed shortly, and then the modern diffusion of products under the information propagation using multiagent simulation is discussed. The remarkable phenomena like “Winner-Takes-All” and “Chasm” can be observed, and one product marketing strategy is also proposed.

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