A Survey of Evolving Models for Weighted Complex Networks based on their Dynamics and Evolution

Weighted Hypernetworks

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we extend the concept of evolving models of complex networks to hypernetworks. In this work, we firstly propose a non-uniform hypernetwork model with attractiveness, and obtain the stationary average hyperdegree distribution of the non-uniform hypernetwork. Furthermore, we develop a model for weighted hypernetworks that couples the establishment of new hyperedges an…

Universality of competitive networks for weighted networks

In this paper, we propose a new model that allows us to investigate this competitive aspect of real networks in quantitative terms. Through theoretical analysis and numerical simulations, we find that the competitive network have the universality for a weighted network. The relation between parameters in the weighted network and the competitiveness in the competitive network is obtained. So we can use the expression of the degree distribution of the competitive model to calculate that and the strength of the weighted network directly. The analytical solution reveals that the degree distributio…

Fast filtering and animation of large dynamic networks

Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted graph and visualize it by either creating a movie, or by streaming it to an interactive network visualization tool. The algorithm is an approximation of exponential sliding time-window that scales linearly with the number of interactions. We compare the algorithm against rectangular and exponential sliding time-window methods. Our network filtering algorith…

Composite Centrality: A Natural Scale for Complex Evolving Networks

We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures providing additional information, while the composite centrality measure tends to the standard normal distribution. This offers a unified scale to measure node and edge centralities for complex evolving networks under a uniform framework. Considering two real-world cases of the world trade web and the world migration web, both during a time span of 40 years…

Challenges on Probabilistic Modeling for Evolving Networks

With the emerging of new networks, such as wireless sensor networks, vehicle networks, P2P networks, cloud computing, mobile Internet, or social networks, the network dynamics and complexity expands from system design, hardware, software, protocols, structures, integration, evolution, application, even to business goals. Thus the dynamics and uncertainty are unavoidable characteristics, which come from the regular network evolution and unexpected hardware defects, unavoidable software errors, incomplete management information and dependency relationship between the entities among the emerging …

Dynamic Network Embedding Survey

Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of evolving graphs but not only the latest network, for preserving both structural and temporal information from the dynamic networks. Due to the lack of comprehensive investigation of them, we give a survey of dynamic network embedding in this paper. Our survey inspects the data model, representation learning technique, evaluation and application of current rela…

Hubs and Clusters in the Evolving U. S. Internal Migration Network

Most nations of the world periodically publish N x N origin-destination tables, recording the number of people who lived in geographic subdivision i at time t and j at t+1. We have developed and widely applied to such national tables and other analogous (weighted, directed) socioeconomic networks, a two-stage--double-standardization and (strong component) hierarchical clustering--procedure. Previous applications of this methodology and related analytical issues are discussed. Its use is illustrated in a large-scale study, employing recorded United States internal migration flows between the 3,…

Weighted Multiplex Networks

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topolo…

一种用于追踪演化网络中社区的谱框架

A Spectral Framework for Tracking Communities in Evolving Networks

本研究提出一种基于格拉斯曼流形子空间追踪的谱框架，将静态谱社区检测方法推广到时变网络场景，通过块黎曼优化方案实现，在多种类型的合成与真实时序网络中均大幅提升了动态社区检测性能。