scholarly journals Dynamics-Preserving Graph Embedding for Community Mining and Network Immunization

Information ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 250
Author(s):  
Jianan Zhong ◽  
Hongjun Qiu ◽  
Benyun Shi
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Graph Embedding ◽  
Opinion Formation ◽  
Embedding Method ◽  
Influence Matrix ◽  
Singular Value Decomposition Method ◽  
Epidemic Dynamics ◽  
Community Mining ◽  
Node Embeddings

In recent years, the graph embedding approach has drawn a lot of attention in the field of network representation and analytics, the purpose of which is to automatically encode network elements into a low-dimensional vector space by preserving certain structural properties. On this basis, downstream machine learning methods can be implemented to solve static network analytic tasks, for example, node clustering based on community-preserving embeddings. However, by focusing only on structural properties, it would be difficult to characterize and manipulate various dynamics operating on the network. In the field of complex networks, epidemic spreading is one of the most typical dynamics in networks, while network immunization is one of the effective methods to suppress the epidemics. Accordingly, in this paper, we present a dynamics-preserving graph embedding method (EpiEm) to preserve the property of epidemic dynamics on networks, i.e., the infectiousness and vulnerability of network nodes. Specifically, we first generate a set of propagation sequences through simulating the Susceptible-Infectious process on a network. Then, we learn node embeddings from an influence matrix using a singular value decomposition method. Finally, we show that the node embeddings can be used to solve epidemics-related community mining and network immunization problems. The experimental results in real-world networks show that the proposed embedding method outperforms several benchmark methods with respect to both community mining and network immunization. The proposed method offers new insights into the exploration of other collective dynamics in complex networks using the graph embedding approach, such as opinion formation in social networks.

scholarly journals Characterizing the Complexity of Weighted Networks via Graph Embedding and Point Pattern Analysis

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 925
Author(s):  
Shuo Chen ◽  
Zhen Zhang ◽  
Chen Mo ◽  
Qiong Wu ◽  
Peter Kochunov ◽  
...  
Keyword(s):  
Complex Networks ◽  
Pattern Analysis ◽  
Brain Connectivity ◽  
Graph Embedding ◽  
Point Pattern Analysis ◽  
Point Pattern ◽  
Healthy Controls ◽  
Weighted Networks ◽  
The Difference ◽  
Weighted Complex Networks

We propose a new metric to characterize the complexity of weighted complex networks. Weighted complex networks represent a highly organized interactive process, for example, co-varying returns between stocks (financial networks) and coordination between brain regions (brain connectivity networks). Although network entropy methods have been developed for binary networks, the measurement of non-randomness and complexity for large weighted networks remains challenging. We develop a new analytical framework to measure the complexity of a weighted network via graph embedding and point pattern analysis techniques in order to address this unmet need. We first perform graph embedding to project all nodes of the weighted adjacency matrix to a low dimensional vector space. Next, we analyze the point distribution pattern in the projected space, and measure its deviation from the complete spatial randomness. We evaluate our method via extensive simulation studies and find that our method can sensitively detect the difference of complexity and is robust to noise. Last, we apply the approach to a functional magnetic resonance imaging study and compare the complexity metrics of functional brain connectivity networks from 124 patients with schizophrenia and 103 healthy controls. The results show that the brain circuitry is more organized in healthy controls than schizophrenic patients for male subjects while the difference is minimal in female subjects. These findings are well aligned with the established sex difference in schizophrenia.

scholarly journals Py3plex toolkit for visualization and analysis of multilayer networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Blaž Škrlj ◽  
Jan Kralj ◽  
Nada Lavrač
Keyword(s):  
Complex Networks ◽  
Temporal Change ◽  
Real Life ◽  
Analysis Software ◽  
Multilayer Networks ◽  
Speed Up ◽  
Node Embeddings ◽  
Synthetic Networks

Abstract Complex networks are used as means for representing multimodal, real-life systems. With increasing amounts of data that lead to large multilayer networks consisting of different node and edge types, that can also be subject to temporal change, there is an increasing need for versatile visualization and analysis software. This work presents a lightweight Python library, Py3plex, which focuses on the visualization and analysis of multilayer networks. The library implements a set of simple graphical primitives supporting intra- as well as inter-layer visualization. It also supports many common operations on multilayer networks, such as aggregation, slicing, indexing, traversal, and more. The paper also focuses on how node embeddings can be used to speed up contemporary (multilayer) layout computation. The library’s functionality is showcased on both real and synthetic networks.

scholarly journals Degree difference: a simple measure to characterize structural heterogeneity in complex networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Amirhossein Farzam ◽  
Areejit Samal ◽  
Jürgen Jost
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Degree Sequence ◽  
Structural Heterogeneity ◽  
Local Network ◽  
Basic Unit ◽  
Local Geometry ◽  
Scale Free ◽  
Mixing Patterns ◽  
Topological Robustness

AbstractDespite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, ‘degree difference’ (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measures in network science. Typically, edges with different DD play different structural roles and the DD distribution is an important network signature. Notably, DD is the basic unit of assortativity. We provide an explanation as to why DD can characterize structural heterogeneity in mixing patterns unlike global assortativity and local node assortativity. By analyzing synthetic and real networks, we show that DD distribution can be used to distinguish between different types of networks including those networks that cannot be easily distinguished using degree sequence and global assortativity. Moreover, we show DD to be an indicator for topological robustness of scale-free networks. Overall, DD is a local measure that is simple to define, easy to evaluate, and that reveals structural properties of networks not readily seen from other measures.

scholarly journals Macro- and mesoscale pattern interdependencies in complex networks

2019 ◽  
Vol 16 (159) ◽  
pp. 20190553 ◽  
Author(s):  
M. J. Palazzi ◽  
J. Borge-Holthoefer ◽  
C. J. Tessone ◽  
A. Solé-Ribalta
Keyword(s):  
Complex Networks ◽  
Empirical Evidence ◽  
Structural Properties ◽  
Modular Architecture ◽  
Modular Networks ◽  
As Species ◽  
Species Abundances ◽  
Organizational Patterns ◽  
Natural Combination ◽  
The Relationship

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other arrangements—e.g. nestedness or core–periphery—have been studied in parallel, but to a much lesser extent. However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from distinct organizations at different scales. Here, we explore the relationship between some of these different organizational patterns: two at the mesoscale (modularity and in-block nestedness); and one at the macroscale (nestedness). We show experimentally and analytically that nestedness imposes bounds to modularity, with exact analytical results in idealized scenarios. Specifically, we show that nestedness and modularity are interdependent. Furthermore, we analytically evidence that in-block nestedness provides a natural combination between nested and modular networks, taking structural properties of both. Far from a mere theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy dynamical effects on processes, such as species abundances and stability in ecology.

Efficient weighting strategy for enhancing synchronizability of complex networks

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
Youquan Wang ◽  
Feng Yu ◽  
Shucheng Huang ◽  
Juanjuan Tu ◽  
Yan Chen
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Real World ◽  
Centrality Measures ◽  
Node Degree ◽  
Scale Free ◽  
High Propensity ◽  
Network Link ◽  
Weighting Strategy ◽  
Weighting Methods

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world networks.

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