An Introduction to Complex Networks

2013 ◽  
Author(s):  
Jordi Bascompte ◽  
Pedro Jordano
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Network Structure ◽  
Ecological Networks ◽  
Broad Context ◽  
Network Approach ◽  
Mutualistic Networks ◽  
Plant Animal Interactions

Mutualisms can involve dozens, even hundreds, of species and this complexity has precluded a serious community-wide approach to plant–animal interactions. The most straightforward way to describe such an interacting community is with a network of interactions. In this approach, species are represented as nodes of two types: plants and animals. This chapter provides the tools and concepts for characterizing mutualistic networks and placing them into a broad context. This serves as a background with which to understand the structure of mutualistic networks. The discussions cover a network approach to complex systems, measures of network structure, models of network buildup, and ecological networks.

scholarly journals Dynamics in Complex Systems

2009 ◽  
Vol 17 (2) ◽  
pp. 357-370 ◽  
Author(s):  
J. Kurths ◽  
D. Maraun ◽  
C. S. Zhou ◽  
G. Zamora-Lopez ◽  
Y. Zou
Keyword(s):  
Earth Sciences ◽  
Complex Systems ◽  
Complex Networks ◽  
Structural Properties ◽  
Topological Structure ◽  
Statistical Physics ◽  
Complex Dynamics ◽  
Mathematical Statistics ◽  
Brain Dynamics ◽  
Network Approach

Over the last decade, we have witnessed the birth of a new movement of interest and research in the study of complex networks. These networks often have irregular structural properties, but also encompass rich dynamics. The interplay between the network topological structure and the associated dynamics attracts a lot of interest. In this research line, we propose a network approach to dealing with complex dynamics, in particular with synchronization dynamics. From the methodological perspective, this approach requires novel ideas from nonlinear sciences, statistical physics and mathematical statistics. Furthermore, we show applications in different disciplines, from earth sciences to brain dynamics. The complex network’s approach is an interdisciplinary topic and could be promising for the understanding of complexity from a systems level.

Networks

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.

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 New Inequalities between Information Measures of Network Information Content

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Pantelimon-George Popescu ◽  
Florin Pop ◽  
Alexandru Herişanu ◽  
Nicolae Ţăpuş
Keyword(s):  
Information Processing ◽  
Complex Systems ◽  
Complex Networks ◽  
Information Content ◽  
Discrete Case ◽  
Network Information ◽  
Information Inequalities ◽  
Information Measures ◽  
New Inequalities

We refine a classical logarithmic inequality using a discrete case of Bernoulli inequality, and then we refine furthermore two information inequalities between information measures for graphs, based on information functionals, presented by Dehmer and Mowshowitz in (2010) as Theorems 4.7 and 4.8. The inequalities refer to entropy-based measures of network information content and have a great impact for information processing in complex networks (a subarea of research in modeling of complex systems).

Improved influential nodes identification in complex networks

2021 ◽  
pp. 1-9
Author(s):  
Shi Dong ◽  
Wengang Zhou
Keyword(s):  
Theoretical Analysis ◽  
Complex Networks ◽  
Network Structure ◽  
Information Entropy ◽  
Network System ◽  
Weighted Degree ◽  
Identification Methods ◽  
Hybrid Mechanism ◽  
Influential Nodes ◽  
Influential Node

Influential node identification plays an important role in optimizing network structure. Many measures and identification methods are proposed for this purpose. However, the current network system is more complex, the existing methods are difficult to deal with these networks. In this paper, several basic measures are introduced and discussed and we propose an improved influential nodes identification method that adopts the hybrid mechanism of information entropy and weighted degree of edge to improve the accuracy of identification (Hm-shell). Our proposed method is evaluated by comparing with nine algorithms in nine datasets. Theoretical analysis and experimental results on real datasets show that our method outperforms other methods on performance.

scholarly journals The interconnection exchange and complex systems properties in power grid network

2021 ◽  
Vol 336 ◽  
pp. 05020
Author(s):  
Piotr Hadaj ◽  
Marek Nowak ◽  
Dominik Strzałka
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Real Data ◽  
Electrical Energy ◽  
Significant Drop ◽  
Average Efficiency ◽  
Grid Network ◽  
System Operator ◽  
Energy Network

A case study based on the real data obtained from the Polish PSE System Operator of the highest voltages electrical energy network is shown. The data about the interconnection exchange and some complex networks (graphs) parameters were examined, after the removal of selected nodes. This allowed to test selected network parameters and to show that the breakdown of only three nodes in this network can cause significant drop of its average efficiency.

scholarly journals Reconstruction of plant–pollinator networks from observational data

2019 ◽  
Author(s):  
Jean-Gabriel Young ◽  
Fernanda S. Valdovinos ◽  
M. E. J. Newman
Keyword(s):  
Food Webs ◽  
Observational Data ◽  
Network Structure ◽  
Rare Species ◽  
Statistical Technique ◽  
Ecological Networks ◽  
Statistical Analyses ◽  
Published Data ◽  
Statistical Errors ◽  
Plant Pollinator

Empirical measurements of ecological networks such as food webs and mutualistic networks are often rich in structure but also noisy and error-prone, particularly for rare species for which observations are sparse. Focusing on the case of plant–pollinator networks, we here describe a Bayesian statistical technique that allows us to make accurate estimates of network structure and ecological metrics from such noisy observational data. Our method yields not only estimates of these quantities, but also estimates of their statistical errors, paving the way for principled statistical analyses of ecological variables and outcomes. We demonstrate the use of the method with an application to previously published data on plant–pollinator networks in the Seychelles archipelago, calculating estimates of network structure, network nestedness, and other characteristics.

Self-Organization in Multiplex Networks

2018 ◽  
pp. 148-158
Author(s):  
Nikos E. Kouvaris ◽  
Albert Díaz-Guilera
Keyword(s):  
Complex Systems ◽  
Network Structure ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Self Organization ◽  
Multiplex Networks ◽  
The Way

The chapter “Self-Organization in Multiplex Networks” discusses the use of multiplex networks in studying complex systems and synchronization. An important question in the research of complex systems concerns the way the network structure shapes the hosted dynamics and leads to a plethora of self-organization phenomena. Complex systems consist of nodes having some intrinsic dynamics, usually nonlinear, and are connected through the links of the network. Such systems can be studied by means of discrete reaction–diffusion equations; reaction terms account for the dynamics in the nodes, whereas diffusion terms describe the coupling between them. This chapter discusses how multiplex networks are suitable for studying such systems by providing two illustrative examples of self-organization phenomena occurring in them.

Sign in / Sign up

Export Citation Format

Share Document