scholarly journals A simple differential geometry for complex networks

2020 ◽  
pp. 1-28
Author(s):  
Emil Saucan ◽  
Areejit Samal ◽  
Jürgen Jost
Keyword(s):  
Differential Geometry ◽  
Complex Networks ◽  
Ricci Curvature ◽  
Real World ◽  
Large Scale ◽  
Metric Spaces ◽  
Geodesic Curvature ◽  
Higher Dimensional ◽  
Large Scale Networks ◽  
Bonnet Theorem

Abstract We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particular, the proposed curvatures based on the interpretation of Haantjes definition as geodesic curvature allow us to give a network analogue of the classical local Gauss–Bonnet theorem. Furthermore, we propose even simpler and more intuitive proxies for the Haantjes curvature that allow for even faster and easier computations in large-scale networks. In addition, we also investigate the embedding properties of the proposed Ricci curvatures. Lastly, we also investigate the behavior, both on model and real-world networks, of the curvatures introduced herein with more established notions of Ricci curvature and other widely used network measures.

A new spectral coarse-graining algorithm based on K-means clustering in complex networks

2019 ◽  
Vol 33 (01) ◽  
pp. 1850421 ◽  
Author(s):  
Lang Zeng ◽  
Zhen Jia ◽  
Yingying Wang
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Dynamic Properties ◽  
Coarse Graining ◽  
Kuramoto Model ◽  
Coarse Grained ◽  
Original Network ◽  
Topological Information ◽  
Real World Applications ◽  
Large Scale Networks

Coarse-graining of complex networks is one of the important algorithms to study large-scale networks, which is committed to reducing the size of networks while preserving some topological information or dynamic properties of the original networks. Spectral coarse-graining (SCG) is one of the typical coarse-graining algorithms, which can keep the synchronization ability of the original network well. However, the calculation of SCG is large, which limits its real-world applications. And it is difficult to accurately control the scale of the coarse-grained network. In this paper, a new SCG algorithm based on K-means clustering (KCSCG) is proposed, which cannot only reduce the amount of calculation, but also accurately control the size of coarse-grained network. At the same time, KCSCG algorithm has better effect in keeping the network synchronization ability than SCG algorithm. A large number of numerical simulations and Kuramoto-model example on several typical networks verify the feasibility and effectiveness of the proposed algorithm.

scholarly journals Identifying Node Importance in a Complex Network Based on Node Bridging Feature

2018 ◽  
Vol 8 (10) ◽  
pp. 1914 ◽  
Author(s):  
Lincheng Jiang ◽  
Yumei Jing ◽  
Shengze Hu ◽  
Bin Ge ◽  
Weidong Xiao
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Shortest Paths ◽  
Evaluation Criteria ◽  
Local Network ◽  
Network Efficiency ◽  
Network Attack ◽  
Node Importance ◽  
Pass Through ◽  
Large Scale Networks

Identifying node importance in complex networks is of great significance to improve the network damage resistance and robustness. In the era of big data, the size of the network is huge and the network structure tends to change dynamically over time. Due to the high complexity, the algorithm based on the global information of the network is not suitable for the analysis of large-scale networks. Taking into account the bridging feature of nodes in the local network, this paper proposes a simple and efficient ranking algorithm to identify node importance in complex networks. In the algorithm, if there are more numbers of node pairs whose shortest paths pass through the target node and there are less numbers of shortest paths in its neighborhood, the bridging function of the node between its neighborhood nodes is more obvious, and its ranking score is also higher. The algorithm takes only local information of the target nodes, thereby greatly improving the efficiency of the algorithm. Experiments performed on real and synthetic networks show that the proposed algorithm is more effective than benchmark algorithms on the evaluation criteria of the maximum connectivity coefficient and the decline rate of network efficiency, no matter in the static or dynamic attack manner. Especially in the initial stage of attack, the advantage is more obvious, which makes the proposed algorithm applicable in the background of limited network attack cost.

scholarly journals An Efficient Partition-Based Approach to Identify and Scatter Multiple Relevant Spreaders in Complex Networks

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1216
Author(s):  
Jedidiah Yanez-Sierra ◽  
Arturo Diaz-Perez ◽  
Victor Sosa-Sosa
Keyword(s):  
Complex Networks ◽  
Information Diffusion ◽  
Large Scale ◽  
Centrality Measures ◽  
Correct Identification ◽  
Graph Analysis ◽  
Relevant Role ◽  
Two Phases ◽  
Large Scale Networks ◽  
Spreading Processes

One of the main problems in graph analysis is the correct identification of relevant nodes for spreading processes. Spreaders are crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases, rumors, and more. Correct identification of spreaders in graph analysis is a relevant task to optimally use the network structure and ensure a more efficient flow of information. Additionally, network topology has proven to play a relevant role in the spreading processes. In this sense, more of the existing methods based on local, global, or hybrid centrality measures only select relevant nodes based on their ranking values, but they do not intentionally focus on their distribution on the graph. In this paper, we propose a simple yet effective method that takes advantage of the underlying graph topology to guarantee that the selected nodes are not only relevant but also well-scattered. Our proposal also suggests how to define the number of spreaders to select. The approach is composed of two phases: first, graph partitioning; and second, identification and distribution of relevant nodes. We have tested our approach by applying the SIR spreading model over nine real complex networks. The experimental results showed more influential and scattered values for the set of relevant nodes identified by our approach than several reference algorithms, including degree, closeness, Betweenness, VoteRank, HybridRank, and IKS. The results further showed an improvement in the propagation influence value when combining our distribution strategy with classical metrics, such as degree, outperforming computationally more complex strategies. Moreover, our proposal shows a good computational complexity and can be applied to large-scale networks.

scholarly journals Higher Dimensional Consensus: Learning in Large-Scale Networks

2010 ◽  
Vol 58 (5) ◽  
pp. 2836-2849 ◽  
Author(s):  
Usman A. Khan ◽  
Soummya Kar ◽  
José M. F. Moura
Keyword(s):  
Large Scale ◽  
Higher Dimensional ◽  
Large Scale Networks

scholarly journals Research on Community Detection in Complex Networks Based on Internode Attraction

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1383
Author(s):  
Jinfang Sheng ◽  
Cheng Liu ◽  
Long Chen ◽  
Bin Wang ◽  
Junkai Zhang
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Community Detection ◽  
Large Scale ◽  
Rapid Development ◽  
Structure Detection ◽  
Detection Approach ◽  
Real World Datasets ◽  
New Community ◽  
Large Scale Networks

With the rapid development of computer technology, the research on complex networks has attracted more and more attention. At present, the research directions of cloud computing, big data, internet of vehicles, and distributed systems with very high attention are all based on complex networks. Community structure detection is a very important and meaningful research hotspot in complex networks. It is a difficult task to quickly and accurately divide the community structure and run it on large-scale networks. In this paper, we put forward a new community detection approach based on internode attraction, named IACD. This algorithm starts from the perspective of the important nodes of the complex network and refers to the gravitational relationship between two objects in physics to represent the forces between nodes in the network dataset, and then perform community detection. Through experiments on a large number of real-world datasets and synthetic networks, it is shown that the IACD algorithm can quickly and accurately divide the community structure, and it is superior to some classic algorithms and recently proposed algorithms.

scholarly journals Algorithms for generating large-scale clustered random graphs

2014 ◽  
Vol 2 (3) ◽  
pp. 403-415 ◽  
Author(s):  
CHENG WANG ◽  
OMAR LIZARDO ◽  
DAVID HACHEN
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Real World ◽  
Local Structure ◽  
Topological Structure ◽  
Large Scale ◽  
Random Processes ◽  
Clustering Coefficient ◽  
Computation Efficiency ◽  
Large Scale Networks

AbstractReal-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure beyond the dyadic level. As a result we need to generate clustered random graph to compare the local structure at higher network levels. In this paper a generalized version of Gleeson's algorithm G(VS, VT, ES, ET, S, T) is advanced to generate a clustered random graph in large-scale which persists the number of vertices |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network and it works successfully for nine large-scale networks. Our new algorithm also has advantages in randomness evaluation and computation efficiency when compared with the existing algorithms.

A UNIFIED COMMUNITY DETECTION ALGORITHM IN LARGE-SCALE COMPLEX NETWORKS

2019 ◽  
Vol 22 (03) ◽  
pp. 1950004
Author(s):  
HAO LONG ◽  
XIAO-WEI LIU
Keyword(s):  
Complex Networks ◽  
Community Detection ◽  
Large Scale ◽  
Detection Algorithm ◽  
Component Structure ◽  
Overlapping Communities ◽  
Expansion Strategy ◽  
High Scalability ◽  
Community Detection Algorithm ◽  
Large Scale Networks

A community is the basic component structure of complex networks and is important for network analysis. In recent decades, researchers from different fields have witnessed a boom of community detection, and many algorithms were proposed to retrieve disjoint or overlapping communities. In this paper, a unified expansion approach is proposed to obtain two different network partitions, which can provide divisions with higher accuracies and have high scalability in large-scale networks. First, we define the edge intensity to quantify the densities of network edges, a higher edge intensity indicates a more compact pair of nodes. Second, vertices of higher density edges are extracted out and denoted as core nodes, whereas other vertices are treated as margin nodes; finally we apply an expansion strategy to form disjoint communities: closely connected core nodes are combined as disjoint skeleton communities, and margin nodes are gradually attached to the nearest skeleton communities. To detect overlapping communities, extra steps are adopted: potential overlapping nodes are identified from the existing disjoint communities and replicated; and communities that bear replicas are further partitioned into smaller clusters. Because replicas of potential overlapping nodes might remain in different communities, overlapping communities can be acquired. Experimental results on real and synthetic networks illustrate higher accuracy and better performance of our method.

Uncovering the fuzzy community structure accurately based on steepest descent projection

2017 ◽  
Vol 31 (27) ◽  
pp. 1750249 ◽  
Author(s):  
Changjian Fang ◽  
Dejun Mu ◽  
Zhenghong Deng ◽  
Jiaqi Yan
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Large Scale ◽  
Steepest Descent ◽  
Topological Information ◽  
Generalized Framework ◽  
Open Question ◽  
Fuzzy C Means Algorithm

Uncovering the community structure in complex network is a hot research point in recent years. How to identify the community structure accurately in complex network is still an open question under research. There are lots of methods based on topological information, which have some good performances at the expense of longer runtimes. In this paper, we propose a new fuzzy algorithm which follows the line of fuzzy c-means algorithm. A steepest descent framework with projection by optimizing the quality function is presented under the generalized framework. The results of experiments on both real-world networks and synthetic networks show that the proposed method achieves the highest efficiency and is easy for detecting fuzzy community structure in large-scale complex networks.

scholarly journals Modified Lomax model: a heavy-tailed distribution for fitting large-scale real-world complex networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Swarup Chattopadhyay ◽  
Tanujit Chakraborty ◽  
Kuntal Ghosh ◽  
Asit K. Das
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Large Scale ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

scholarly journals Local dependency in networks

2015 ◽  
Vol 25 (2) ◽  
pp. 281-293 ◽  
Author(s):  
Miloš Kudĕlka ◽  
Šárka Zehnalová ◽  
Zdenĕk Horák ◽  
Pavel Krömer ◽  
Václav Snášel
Keyword(s):  
Real World ◽  
Large Scale ◽  
Real World Data ◽  
High Quality ◽  
High Effectiveness ◽  
Local Dependency ◽  
Node Ranking ◽  
Large Scale Networks ◽  
The Relationship ◽  
Entire Network

Abstract Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network’s nodes from the structure in local surroundings of individual nodes. For the tasks we deal with in this article, the key technical parameter is locality. Since only the surroundings of the examined nodes are used in computations, there is no need to analyze the entire network. This allows the application of our approach in the area of large-scale networks. We present several experiments using small networks as well as large-scale artificial and real world networks. The results of the experiments show high effectiveness due to the locality of our approach and also high quality node ranking comparable to PageRank.

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