scholarly journals On the asymptotic behavior of the average geodesic distance L and the compactness CB of simple connected undirected graphs whose order approaches infinity

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259776
Author(s):  
Tatiana Lokot ◽  
Olga Abramov ◽  
Alexander Mehler
Keyword(s):  
Asymptotic Behavior ◽  
Network Theory ◽  
Geodesic Distance ◽  
Structural Complexity ◽  
Undirected Graphs ◽  
Information Theoretic ◽  
Complex Network Theory ◽  
Theoretic Classification ◽  
Real World Problems

The average geodesic distance L Newman (2003) and the compactness CB Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple connected undirected graphs G of order n, we study the behavior of L(G) and CB(G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and CB(G) lies within the interval [0;1/3] and [2/3;1], respectively. Moreover, for any not necessarily rational number β ∈ [0;1/3] (α ∈ [2/3;1]) we show how to construct the sequence of graphs {G}, |V(G)| = n → ∞, for which the limit of L(G)/n (CB(G)) is exactly β (α) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.

An information-theoretic classification of amino acids for the assessment of interfaces in protein–protein docking

2013 ◽  
Vol 19 (9) ◽  
pp. 3901-3910 ◽  
Author(s):  
Christophe Jardin ◽  
Arno G. Stefani ◽  
Martin Eberhardt ◽  
Johannes B. Huber ◽  
Heinrich Sticht
Keyword(s):  
Amino Acids ◽  
Protein Docking ◽  
Information Theoretic ◽  
Theoretic Classification

scholarly journals Complex Network Theory for Water Distribution Networks Analysis

10.29007/w1bk ◽  
2018 ◽  
Author(s):  
Antonietta Simone ◽  
Luca Ridolfi ◽  
Luigi Berardi ◽  
Daniele Laucelli ◽  
Orazio Giustolisi
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Path Length ◽  
Water Distribution ◽  
Distribution Networks ◽  
Networked Systems ◽  
Clustering Coefficient ◽  
Complex Network Theory ◽  
Connectivity Structure

Performance of networked systems greatly depends on their topologic or connectivity structure. Nowadays, the analysis of the relevant features influencing the emerging behavior of networked systems is possible because of the increasing computational power and availability of information. Complex Network Theory classifies the connectivity structures of real systems using the nodal degree, the average path length, the clustering coefficient and the probability of connection. However, networked city infrastructures, e.g. water distribution networks (WDNs), are constrained by the spatial characteristics of the environment where they are laid. Therefore, networked infrastructures are classified as spatial networks and the classification of their connectivity structure requires a modification of the classic framework. To this purpose, the paper proposes a classification of WDNs using the neighbourhood nodal degree instead of the classic degree, the network size instead of the probability of connection and the classic average path length. The research will show that the clustering coefficient is not useful to describe the behavior of these constrained systems.

scholarly journals Ecological Network Optimization in Urban Central District Based on Complex Network Theory: A Case Study with the Urban Central District of Harbin

2021 ◽  
Vol 18 (4) ◽  
pp. 1427
Author(s):  
Shuang Song ◽  
Dawei Xu ◽  
Shanshan Hu ◽  
Mengxi Shi
Keyword(s):  
Complex Network ◽  
Network Optimization ◽  
Network Theory ◽  
Habitat Destruction ◽  
Landscape Patterns ◽  
Ecological Network ◽  
Complex Network Theory ◽  
Ecological Corridors ◽  
Low Degree ◽  
Central District

Habitat destruction and declining ecosystem service levels caused by urban expansion have led to increased ecological risks in cities, and ecological network optimization has become the main way to resolve this contradiction. Here, we used landscape patterns, meteorological and hydrological data as data sources, applied the complex network theory, landscape ecology, and spatial analysis technology, a quantitative analysis of the current state of landscape pattern characteristics in the central district of Harbin was conducted. The minimum cumulative resistance was used to extract the ecological network of the study area. Optimized the ecological network by edge-adding of the complex network theory, compared the optimizing effects of different edge-adding strategies by using robustness analysis, and put forward an effective way to optimize the ecological network of the study area. The results demonstrate that: The ecological patches of Daowai, Xiangfang, Nangang, and other old districts in the study area are small in size, fewer in number, strongly fragmented, with a single external morphology, and high internal porosity. While the ecological patches in the new districts of Songbei, Hulan, and Acheng have a relatively good foundation. And ecological network connectivity in the study area is generally poor, the ecological corridors are relatively sparse and scattered, the connections between various ecological sources of the corridors are not close. Comparing different edge-adding strategies of complex network theory, the low-degree-first strategy has the most outstanding performance in the robustness test. The low-degree-first strategy was used to optimize the ecological network of the study area, 43 ecological corridors are added. After the optimization, the large and the small ecological corridors are evenly distributed to form a complete network, the optimized ecological network will be significantly more connected, resilient, and resistant to interference, the ecological flow transmission will be more efficient.

Patterns of interpredictability and principal parts in Latin verb paradigms: an entropy-based approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Matteo Pellegrini
Keyword(s):  
Principal Part ◽  
Quantitative Approach ◽  
Information Theoretic ◽  
Verb Inflection ◽  
Type Frequency ◽  
Principal Parts ◽  
The Impact

AbstractThis paper provides a fully word-based, abstractive analysis of predictability in Latin verb paradigms. After reviewing previous traditional and theoretically grounded accounts of Latin verb inflection, a procedure is outlined where the uncertainty in guessing the content of paradigm cells given knowledge of one or more inflected wordforms is measured by means of the information-theoretic notions of unary and n-ary implicative entropy, respectively, in a quantitative approach that uses the type frequency of alternation patterns between wordforms as an estimate of their probability of application. Entropy computations are performed by using the Qumin toolkit on data taken from the inflected lexicon LatInfLexi. Unary entropy values are used to draw a mapping of the verbal paradigm in zones of full interpredictability, composed of cells that can be inferred from one another with no uncertainty. N-ary entropy values are used to extract categorical and near principal part sets, that allow to fill the rest of the paradigm with little or no uncertainty. Lastly, the issue of the impact of information on the derivational relatedness of lexemes on uncertainty in inflectional predictions is tackled, showing that adding a classification of verbs in derivational families allows for a relevant reduction of entropy, not only for derived verbs, but also for simple ones.

Taxonomical Classification of Web Usage Mining Applications and its Ontological Representation

2018 ◽  
Vol 7 (3) ◽  
pp. 39-43
Author(s):  
Satyaveer Singh ◽  
Mahendra Singh Aswal
Keyword(s):  
Web Usage Mining ◽  
Web Usage ◽  
Navigation Patterns ◽  
Product Recommendations ◽  
Taxonomical Classification ◽  
The Comparative Study ◽  
The Web ◽  
Real World Problems

Web usage mining is used to find out fascinating consumer navigation patterns which can be applied to a lot of real-world problems, such as enriching websites or pages, generating newly topic or product recommendations and consumer behavior studies, etc. In this paper, an attempt has been made to provide a taxonomical classification of web usage mining applications with two levels of hierarchy. Further, the ontology for various categories of the web usage mining applications has been developed and to prove the completeness of proposed taxonomy, a rigorous case study has been performed. The comparative study with other existing classifications of web usage mining applications has also been performed.

Sign in / Sign up

Export Citation Format

Share Document