• Corpus ID: 2954193

Continuous and robust clustering coefficients for weighted and directed networks

  title={Continuous and robust clustering coefficients for weighted and directed networks},
  author={Kent Miyajima and Takashi Sakuragawa},
We introduce new clustering coefficients for weighted networks. They are continuous and robust against edge weight changes. Recently, generalized clustering coefficients for weighted and directed networks have been proposed. These generalizations have a common property, that their values are not continuous. They are sensitive with edge weight changes, especially at zero weight. With these generalizations, if vanishingly low weights of edges are truncated to weight zero for some reason, the… 

Comparison of Different Generalizations of Clustering Coefficient and Local Efficiency for Weighted Undirected Graphs

The best generalization of the clustering coefficient is , defined in Miyajima and Sakuragawa (2014), while the best generalizations of the local efficiency is , proposed in this letter.

Weighted directed clustering: interpretations and requirements for heterogeneous, inferred, and measured networks

This work proposes a fully-weighted continuous clustering coefficient that satisfies all the previously proposed criteria while also being continuous with respect to vanishing weights and demonstrates that the behavior and meaning of the Zhang–Horvath clustering and the new continuous definition provide complementary results and significantly outperform other definitions in multiple relevant conditions.

Introducing Graph Cumulants: What is the Kurtosis of your Social Network?

In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are

Energy-Efficient Ant Colony-Based k-Hop Clustering and Transmission Range Assignment Protocol for Connectivity Construction in Dense Wireless Sensor Networks

This paper proposes an ant colony-based asynchronous and localized protocol that helps to significantly reduce energy losses by simultaneously eliminating redundant and poor quality links, always keeping the Cluster Head-to-member distance up to k-hops and minimizing signalization.

Network level characteristics in the emotion recognition network after unilateral temporal lobe surgery

It is concluded that the emotion recognition network is robust and functionally able to compensate for structural damage without substantial global reorganization, in line with a psychological construction theory.

Self-stabilising hybrid connectivity control protocol for WSNs

The authors propose a localised and asynchronous self-stabilising hybrid message passing a solution that seamlessly merges three well known connectivity control techniques for such ad hoc networks, namely k -hop clustering, power control (transmission range adjustment) and sleep/wake scheduling.



Clustering Coefficients for Weighted Networks ∗ †

A natural and transparent derivation of this clustering coefficient is given and it is found that the weighted clustering and degree distributions reveal global topological differences between normal and tumour networks.

A New Methodology for Generalizing Unweighted Network Measures

The effective cardinality is defined, a new metric that quantifies how many edges are effectively being used, assuming that an edge’s weight reflects the amount of interaction across that edge, and it is proved that a generalized measure, using the method, reduces to the original unweighted measure if there is no disparity between weights.

Intensity and coherence of motifs in weighted complex networks.

This paper applies motif scores and clustering coefficient to financial and metabolic networks and finds that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.

Clustering in complex directed networks.

  • G. Fagiolo
  • Computer Science, Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
The CC is extended to the case of (binary and weighted) directed networks and its expected value for random graphs is computed and is distinguished between CCs that count all directed triangles in the graph (independently of the direction of their edges) andCCs that only consider particular types of directed triangles (e.g., cycles).

Approximating Clustering Coefficient and Transitivity

A new fast approximation algorithm for the weighted clustering coecient and the transitivity is presented and a simple graph generator algorithm is given that works according to the preferential attachment rule but also generates graphs with adjustable clusteringCoecient.

The architecture of complex weighted networks.

This work studies the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively, and defines appropriate metrics combining weighted and topological observables that enable it to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices.

Ensemble approach to the analysis of weighted networks.

We present an approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks, such as the average degree of the

A General Framework for Weighted Gene Co-Expression Network Analysis

  • Bin ZhangS. Horvath
  • Computer Science
    Statistical applications in genetics and molecular biology
  • 2005
A general framework for `soft' thresholding that assigns a connection weight to each gene pair is described and several node connectivity measures are introduced and provided empirical evidence that they can be important for predicting the biological significance of a gene.

Economic small-world behavior in weighted networks

This paper proposes a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks, and provides an adequate tool to quantitatively analyze the behaviour of complex networks in the real world.

Range-dependent random graphs and their application to modeling large small-world Proteome datasets.

  • P. Grindrod
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
This paper introduces a class of range-dependent graphs, governed by a power law relating intervertex range to edge probability, which are amenable to analysis, and for which macroscopic graph parameters are given by explicit forms.