Modularity and Dynamics on Complex Networks

2021 ◽  
Author(s):  
Renaud Lambiotte ◽  
Michael T. Schaub
Keyword(s):  
Complex Networks ◽  
Network Structure ◽  
Network Dynamics ◽  
Building Blocks ◽  
Point Of View ◽  
Modular Structure ◽  
Dynamical Processes ◽  
Modular Network ◽  
Structure And Dynamics ◽  
Modular Organisation

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on 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.

ENTRAINMENT COMPETITION IN COMPLEX NETWORKS

2010 ◽  
Vol 20 (03) ◽  
pp. 827-833
Author(s):  
I. LEYVA ◽  
I. SENDIÑA-NADAL ◽  
J. A. ALMENDRAL ◽  
J. M. BULDÚ ◽  
D. LI ◽  
...  
Keyword(s):  
Complex Networks ◽  
Network Structure ◽  
New Method ◽  
Simultaneous Presence ◽  
Modular Network ◽  
Overlapping Communities ◽  
Frequency Changes

The response of a random and modular network to the simultaneous presence of two frequencies is considered. The competition for controlling the dynamics of the network results in different behaviors, such as frequency changes or permanent synchronization frustration, which can be directly related to the network structure. From these observations, we propose a new method for detecting overlapping communities in structured networks.

Relevance of network topology for the dynamics of biological neuronal networks

2021 ◽  
Author(s):  
Simachew Abebe Mengiste ◽  
Ad Aertsen ◽  
Arvind Kumar
Keyword(s):  
Network Topology ◽  
Network Structure ◽  
Neuronal Networks ◽  
Network Dynamics ◽  
Clustering Coefficient ◽  
Network Activity ◽  
Structure And Dynamics ◽  
Structure Dynamics ◽  
Non Linear ◽  
Activity Dynamics

Complex random networks provide a powerful mathematical framework to study high-dimensional physical and biological systems. Several features of network structure (e.g. degree correlation, average path length, clustering coefficient) are correlated with descriptors of network dynamics and function. However, it is not clear which features of network structure relate to the dynamics of biological neuronal networks (BNNs), characterized by non-linear nodes with high in- and out degrees, but being weakly connected and communicating in an event-driven manner, i.e. only when neurons spike. To better understand the structure-dynamics relationship in BNNs, we analysed the structure and dynamics of > 9,000 BNNs with different sizes and topologies. In addition, we also studied the effect of network degeneration on neuronal network structure and dynamics. Surprisingly, we found that the topological class (random, small-world, scale-free) was not an indicator of the BNNs activity state as quantified by the firing rate, network synchrony and spiking regularity. In fact, we show that different network topologies could result in similar activity dynamics. Furthermore, in most cases, the network activity changes did not depend on the rules according to which neurons or synapses were pruned from the networks. The analysis of dynamics and structure of the networks we studied revealed that the effective synaptic weight (ESW) was the most crucial feature in predicting the statistics of spiking activity in BNNs. ESW also explained why different synapse and neuron pruning strategies resulted in almost identical effects on the network dynamics. Thus, our findings provide new insights into the structure-dynamics relationships in BNNs. Moreover, we argue that network topology and rules by which BNNs degenerate are irrelevant for BNN activity dynamics. Beyond neuroscience, our results suggest that in large networks with non-linear nodes, the effective interaction strength among the nodes, instead of the topological network class, may be a better predictor of the network dynamics and information flow.

scholarly journals Comparison of Quantitative Morphology of Layered and Arbitrary Patterns: Contrary to Visual Perception, Binary Arbitrary Patterns Are Layered from a Structural Point of View

2021 ◽  
Vol 11 (14) ◽  
pp. 6300
Author(s):  
Igor Smolyar ◽  
Daniel Smolyar
Keyword(s):  
Boolean Function ◽  
Layer Structure ◽  
Central Element ◽  
Morphological Characteristics ◽  
Building Blocks ◽  
Point Of View ◽  
Living Systems ◽  
Seismic Profiles ◽  
Contour Maps ◽  
Anisotropic Layers

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

scholarly journals Data-driven control of complex networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Giacomo Baggio ◽  
Danielle S. Bassett ◽  
Fabio Pasqualetti
Keyword(s):  
Complex Networks ◽  
Network Dynamics ◽  
Noisy Data ◽  
Data Driven ◽  
Control Algorithms ◽  
Optimal Controls ◽  
Network Systems ◽  
The Past ◽  
Efficient Control ◽  
Finite Set

AbstractOur ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice. In this paper we overcome this limitation, and develop a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of data, where the unknown network is stimulated with arbitrary and possibly random inputs. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy data and in the presence of nonlinear dynamics, as they arise in power grid and brain networks.

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 Predicting partially observed processes on temporal networks by Dynamics-Aware Node Embeddings (DyANE)

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Koya Sato ◽  
Mizuki Oka ◽  
Alain Barrat ◽  
Ciro Cattuto
Keyword(s):  
Network Structure ◽  
Machine Learning Algorithms ◽  
Temporal Networks ◽  
Dynamical Processes ◽  
Network Nodes ◽  
Partially Observed ◽  
Low Dimensional ◽  
Vector Representations ◽  
Infectious Disease Dynamics ◽  
Random Times

AbstractLow-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks – rather than of the network structure itself – with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a lossless modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes’ epidemic states in single instances of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.

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.

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