scholarly journals Robustness in Weighted Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yi Zheng ◽  
Fang Liu ◽  
Yong-Wang Gong
Keyword(s):  
Betweenness Centrality ◽  
Cluster Structure ◽  
Small World ◽  
Weighting Scheme ◽  
Clustering Coefficient ◽  
Fixed Degree ◽  
Scale Free ◽  
Optimal Region ◽  
Weighting Strategy ◽  
The One

The vulnerability of complex systems induced by cascade failures revealed the comprehensive interaction of dynamics with network structure. The effect on cascade failures induced by cluster structure was investigated on three networks, small-world, scale-free, and module networks, of which the clustering coefficient is controllable by the random walk method. After analyzing the shifting process of load, we found that the betweenness centrality and the cluster structure play an important role in cascading model. Focusing on this point, properties of cascading failures were studied on model networks with adjustable clustering coefficient and fixed degree distribution. In the proposed weighting strategy, the path length of an edge is designed as the product of the clustering coefficient of its end nodes, and then the modified betweenness centrality of the edge is calculated and applied in cascade model as its weights. The optimal region of the weighting scheme and the size of the survival components were investigated by simulating the edge removing attack, under the rule of local redistribution based on edge weights. We found that the weighting scheme based on the modified betweenness centrality makes all three networks have better robustness against edge attack than the one based on the original betweenness centrality.

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

Survivability of public transit network based on network structure entropy

2015 ◽  
Vol 26 (09) ◽  
pp. 1550104 ◽  
Author(s):  
Bai-Bai Fu ◽  
Lin Zhang ◽  
Shu-Bin Li ◽  
Yun-Xuan Li
Keyword(s):  
Network Model ◽  
Network Structure ◽  
Public Transit ◽  
Small World ◽  
Clustering Coefficient ◽  
Statistical Characteristics ◽  
Network Efficiency ◽  
Transit Network ◽  
Scale Free ◽  
The Public

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

scholarly journals Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

2016 ◽  
Vol 23 (4) ◽  
pp. 241-256 ◽  
Author(s):  
Eleni Daskalaki ◽  
Konstantinos Spiliotis ◽  
Constantinos Siettos ◽  
Georgios Minadakis ◽  
Gerassimos A. Papadopoulos
Keyword(s):  
Hazard Assessment ◽  
Betweenness Centrality ◽  
Small World ◽  
Clustering Coefficient ◽  
Earthquake Catalog ◽  
Short Term ◽  
2009 L’Aquila Earthquake ◽  
Topological Measures ◽  
Network Properties ◽  
Large Earthquakes

Abstract. The monitoring of statistical network properties could be useful for the short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalog of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) for the case of the L'Aquila (Italy) mainshock (Mw = 6.3) of 6 April 2009, we provide evidence that network measures, both global (average clustering coefficient, small-world index) and local (betweenness centrality) ones, could potentially be exploited for forecasting purposes both in time and space. Our results reveal statistically significant increases in the topological measures and a nucleation of the betweenness centrality around the location of the epicenter about 2 months before the mainshock. The results of the analysis are robust even when considering either large or off-centered the main event space windows.

scholarly journals COMPLEX NETWORK ANALYSIS OF LITERARY AND SCIENTIFIC TEXTS

2012 ◽  
Vol 23 (07) ◽  
pp. 1250051 ◽  
Author(s):  
IWONA GRABSKA-GRADZIŃSKA ◽  
ANDRZEJ KULIG ◽  
JAROSŁAW KWAPIEŃ ◽  
STANISŁAW DROŻDŻ
Keyword(s):  
English Language ◽  
Quantitative Difference ◽  
Clustering Coefficient ◽  
Literary Texts ◽  
Scaling Exponent ◽  
Scientific Texts ◽  
Scale Free ◽  
Network Properties ◽  
The One ◽  
Zipf Law

We present results from our quantitative study of statistical and network properties of literary and scientific texts written in two languages: English and Polish. We show that Polish texts are described by the Zipf law with the scaling exponent smaller than the one for the English language. We also show that the scientific texts are typically characterized by the rank-frequency plots with relatively short range of power-law behavior as compared to the literary texts. We then transform the texts into their word-adjacency network representations and find another difference between the languages. For the majority of the literary texts in both languages, the corresponding networks revealed the scale-free structure, while this was not always the case for the scientific texts. However, all the network representations of texts were hierarchical. We do not observe any qualitative and quantitative difference between the languages. However, if we look at other network statistics like the clustering coefficient and the average shortest path length, the English texts occur to possess more clustered structure than do the Polish ones. This result was attributed to differences in grammar of both languages, which was also indicated in the Zipf plots. All the texts, however, show network structure that differs from any of the Watts–Strögatz, the Barabási–Albert, and the Erdös–Rényi architectures.

scholarly journals Complex network theory, streamflow, and hydrometric monitoring system design

2015 ◽  
Vol 19 (7) ◽  
pp. 3301-3318 ◽  
Author(s):  
M. J. Halverson ◽  
S. W. Fleming
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Small World ◽  
Detection Algorithm ◽  
Clustering Coefficient ◽  
Network Stability ◽  
Meteorological Forcing ◽  
Complex Network Theory ◽  
Scale Free ◽  
Seasonal Flow

Abstract. Network theory is applied to an array of streamflow gauges located in the Coast Mountains of British Columbia (BC) and Yukon, Canada. The goal of the analysis is to assess whether insights from this branch of mathematical graph theory can be meaningfully applied to hydrometric data, and, more specifically, whether it may help guide decisions concerning stream gauge placement so that the full complexity of the regional hydrology is efficiently captured. The streamflow data, when represented as a complex network, have a global clustering coefficient and average shortest path length consistent with small-world networks, which are a class of stable and efficient networks common in nature, but the observed degree distribution did not clearly indicate a scale-free network. Stability helps ensure that the network is robust to the loss of nodes; in the context of a streamflow network, stability is interpreted as insensitivity to station removal at random. Community structure is also evident in the streamflow network. A network theoretic community detection algorithm identified separate communities, each of which appears to be defined by the combination of its median seasonal flow regime (pluvial, nival, hybrid, or glacial, which in this region in turn mainly reflects basin elevation) and geographic proximity to other communities (reflecting shared or different daily meteorological forcing). Furthermore, betweenness analyses suggest a handful of key stations which serve as bridges between communities and might be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, small-membership communities which are by definition rare or undersampled relative to other communities, and index stations having large numbers of intracommunity links, while retaining some degree of redundancy to maintain network robustness.

scholarly journals Complex networks, streamflow, and hydrometric monitoring system design

2014 ◽  
Vol 11 (12) ◽  
pp. 13663-13710 ◽  
Author(s):  
M. Halverson ◽  
S. Fleming
Keyword(s):  
Small World ◽  
Detection Algorithm ◽  
Clustering Coefficient ◽  
Network Stability ◽  
Meteorological Forcing ◽  
Coast Mountains ◽  
Scale Free ◽  
Seasonal Flow ◽  
High Betweenness ◽  
Community Detection Algorithm

Abstract. Network theory is applied to an array of streamflow gauges located in the Coast Mountains of British Columbia and Yukon, Canada. The goal of the analysis is to assess whether insights from this branch of mathematical graph theory can be meaningfully applied to hydrometric data, and more specifically, whether it may help guide decisions concerning stream gauge placement so that the full complexity of the regional hydrology is efficiently captured. The streamflow data, when represented as a complex network, has a global clustering coefficient and average shortest path length consistent with small-world networks, which are a class of stable and efficient networks common in nature, but the results did not clearly suggest a scale-free network. Stability helps ensure that the network is robust to the loss of nodes; in the context of a streamflow network, stability is interpreted as insensitivity to station removal at random. Community structure is also evident in the streamflow network. A community detection algorithm identified 10 separate communities, each of which appears to be defined by the combination of its median seasonal flow regime (pluvial, nival, hybrid, or glacial, which in this region in turn mainly reflects basin elevation) and geographic proximity to other communities (reflecting shared or different daily meteorological forcing). Betweenness analyses additionally suggest a handful of key stations which serve as bridges between communities and might therefore be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, as well as small-membership communities which are by definition rare or undersampled relative to other communities, while retaining some degree of redundancy to maintain network robustness.

scholarly journals SZNAJD MODEL WITH SYNCHRONOUS UPDATING ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1149-1161 ◽  
Author(s):  
YU-SONG TU ◽  
A. O. SOUSA ◽  
LING-JIANG KONG ◽  
MU-REN LIU
Keyword(s):  
Complex Networks ◽  
Small World ◽  
System Size ◽  
The State ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Node Degree ◽  
Scale Free ◽  
Free Network ◽  
Formation Step

We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with nonconsensus and the state with complete consensus in several complex networks. Furthermore, by adjusting the network parameters, we find that a large clustering coefficient does not favor development of a consensus. In particular, in the limit of large system size with the initial concentration p =0.5 of opinion +1, a consensus seems to be never reached for the Watts–Strogatz small-world network, when we fix the connectivity k and the rewiring probability ps; nor for the scale-free network, when we fix the minimum node degree m and the triad formation step probability pt.

scholarly journals COMPLEX NETWORK ANALYSIS IN CRICKET: COMMUNITY STRUCTURE, PLAYER'S ROLE AND PERFORMANCE INDEX

2013 ◽  
Vol 16 (08) ◽  
pp. 1350031 ◽  
Author(s):  
SATYAM MUKHERJEE
Keyword(s):  
Community Structure ◽  
Small World ◽  
Clustering Coefficient ◽  
Central Position ◽  
Network Methods ◽  
Sport Teams ◽  
Role Based ◽  
And Performance ◽  
Partnership Network ◽  
The One

This paper describes the applications of network methods for understanding interaction within members of sport teams. We analyze the interaction of batsmen in international cricket matches. We generate batting partnership network (BPN) for different teams and determine the exact values of clustering coefficient, average degree, average shortest path length of the networks and compare them with the Erdös–Rényi model. We observe that the networks display small-world behavior. We find that most connected batsman is not necessarily the most central and most central players are not necessarily the one with high batting averages. We study the community structure of the BPNs and identify each player's role based on inter-community and intra-community links. We observe that Sir DG Bradman, regarded as the best batsman in cricket history does not occupy the central position in the network — the so-called connector hub. We extend our analysis to quantify the performance, relative importance and effect of removing a player from the team, based on different centrality scores.

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