Distinct Clusterings and Characteristic Path Lengths in Dynamic Small-World Networks with Identical Limit Degree Distribution

It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.

Download Full-text

Small-World Networks of corruption

Revista CIFE Lecturas de Economía Social ◽

10.15332/s0124-3551.2015.0026.01 ◽

2016 ◽

Vol 17 (26) ◽

pp. 19

Author(s):

Pablo Morales ◽

Jorge Finke

Keyword(s):

Collective Behavior ◽

Social Ties ◽

Social Contact ◽

Small World ◽

Its Region ◽

System Of Differential Equations ◽

Small World Networks ◽

Sensitivity Functions ◽

Clustered Networks ◽

Path Lengths

<p>Collective behavior forms and spreads through social contact. This thesis introduces a framework for understanding how the structure of social ties may impact the evolution of bribery. We represent relationships as highly clustered networks with small characteristic path lengths (i.e., small-world models having “local” and “long-range” contacts). Based on a principal-agent-client formulation, our model focuses on the effects of clustering on an equilibrium of persistent bribery. Collective outcomes depend on decision-making mechanisms that rely on sensitivity functions, which capture the level of influence between local contacts. Moreover, we represent the evolution of the network as a system of differential equations and identify its region of parameters for which the equilibrium of persistent bribery is stable. Our results show that an increase in clustering tends to decrease the levels of bribery. A more sensitive response to the behavior of neighbors, on the other hand, tends to increase bribery, but only up to a certain point. Beyond this threshold, the expected level of bribery remains constant, despite variations in the structural properties of the network.</p>

Download Full-text

Analysis of Oncogene Protein Structure Using Small World Network Concept

Current Bioinformatics ◽

10.2174/1574893614666191113143840 ◽

2020 ◽

Vol 15 (7) ◽

pp. 732-740

Author(s):

Neetu Kumari ◽

Anshul Verma

Keyword(s):

Amino Acids ◽

Protein Structure ◽

Degree Distribution ◽

Protein Structures ◽

Small World ◽

Extreme Condition ◽

Centrality Measures ◽

Small World Network ◽

Network Concept ◽

Oncogene Protein

Background: The basic building block of a body is protein which is a complex system whose structure plays a key role in activation, catalysis, messaging and disease states. Therefore, careful investigation of protein structure is necessary for the diagnosis of diseases and for the drug designing. Protein structures are described at their different levels of complexity: primary (chain), secondary (helical), tertiary (3D), and quaternary structure. Analyzing complex 3D structure of protein is a difficult task but it can be analyzed as a network of interconnection between its component, where amino acids are considered as nodes and interconnection between them are edges. Objective: Many literature works have proven that the small world network concept provides many new opportunities to investigate network of biological systems. The objective of this paper is analyzing the protein structure using small world concept. Methods: Protein is analyzed using small world network concept, specifically where extreme condition is having a degree distribution which follows power law. For the correct verification of the proposed approach, dataset of the Oncogene protein structure is analyzed using Python programming. Results: Protein structure is plotted as network of amino acids (Residue Interaction Graph (RIG)) using distance matrix of nodes with given threshold, then various centrality measures (i.e., degree distribution, Degree-Betweenness correlation, and Betweenness-Closeness correlation) are calculated for 1323 nodes and graphs are plotted. Conclusion: Ultimately, it is concluded that there exist hubs with higher centrality degree but less in number, and they are expected to be robust toward harmful effects of mutations with new functions.

Download Full-text

Networks

10.1093/oso/9780198821939.003.0004 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Complex Systems ◽

Complex Networks ◽

Phase Diagrams ◽

Community Detection ◽

Network Science ◽

Small World ◽

Small World Networks ◽

Multilayer Networks ◽

Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

Download Full-text

Tracking sinks of atmospheric methane using small world networks

Chemosphere ◽

10.1016/j.chemosphere.2014.10.043 ◽

2014 ◽

Vol 117 ◽

pp. 766-773 ◽

Cited By ~ 3

Author(s):

Chih-Sheng Lee ◽

Pei-Jen Su

Keyword(s):

Small World ◽

Atmospheric Methane ◽

Small World Networks

Download Full-text

The structure of co-publications multilayer network

Computational Social Networks ◽

10.1186/s40649-021-00089-w ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Ghislain Romaric Meleu ◽

Paulin Yonta Melatagia

Keyword(s):

Power Law ◽

Degree Distribution ◽

Preferential Attachment ◽

Small World ◽

Generation Model ◽

Small World Network ◽

Power Law Distribution ◽

Multilayer Networks ◽

Multilayer Network ◽

Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

Download Full-text