Directed clustering in weighted networks: a new perspective

  title={Directed clustering in weighted networks: a new perspective},
  author={Gian Paolo Clemente and Rosanna Grassi},

Clustering coefficients as measures of the complex interactions in a directed multiplex network

The proposed coefficients find successful application in describing the interrelations of the trade network, allowing to disentangle the effects of countries and sectors and jointly consider the interactions between them.

Clustering Coefficients in Weighted Undirected Multilayer Networks

This work provides new local clustering coefficients for multilayer networks, looking at the network from different perspectives depending on the node’s position, as well as a global clustering coefficient for the whole network.

Taxonomy of Cohesion Coefficients for Weighted and Directed Multilayer Networks

This work extends the classical clustering and closure coefficients through the introduction of the clumping coe⬃cient, which generalizes them to incomplete triangles of any type in the more general context of weighted directed multilayer networks.

Measuring the Clustering Strength of a Network via the Normalized Clustering Coefficient

In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network

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.

Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks

It is shown that, like graphs, stream graphs may be extended to cope with bipartite structures, with node and link weights, or with link directions, and that obtained concepts are consistent with graph and stream graph ones.

Stratified communities in complex business networks

Community structure extraction in directed network using triads

This paper proposes an in-seed-centric scheme based on directed triads and proposes a new metric of the communities' quality based on the triad density of communities, which has better performance on triad-based density over some state-of-the-art methods.

Multi-criteria community detection in International Trade Network

A new algorithm to detect communities by solving the NP-hard CP-problem is introduced, in which weights are determined taking into account all the topological indicators in a multi-criteria approach.

A novel measure of edge and vertex centrality for assessing robustness in complex networks

In this work, we propose a novel robustness measure for networks, which we refer to as Effective Resistance Centrality of a vertex (or an edge), defined as the relative drop of the Kirchhoff index



Clustering in weighted networks

Generalizations of the clustering coefficient to weighted complex networks.

A comparative study of the several suggestions of the clustering coefficient, which is one of the central characteristics in the complex network theory, is presented.

A clustering coefficient for complete weighted networks

For this situation, the concept of clustering is redefined, and computational techniques are presented for computing an associated clustering coefficient for complete weighted undirected or directed networks.

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).

Corrected overlap weight and clustering coefficient

  • V. Batagelj
  • Mathematics
    Lecture Notes in Social Networks
  • 2019
Two well-known network measures: the overlap weight of an edge and the clustering coefficient of a node are discussed and it is shown how the definitions of these measures can be corrected in such a way that they give the expected results.

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.

Directed or Undirected? A New Index to Check for Directionality of Relations in Socio-Economic Networks

A new index is introduced that satisfies two main properties: it can be applied to both binary or weighted graphs, and once suitably standardized, it distributes as a standard normal over all possible adjacency/weights matrices.

Extending the definition of modularity to directed graphs with overlapping communities

This paper starts from the definition of a modularity function, given by Newman to evaluate the goodness of network community decompositions, and extends it to the more general case of directed graphs with overlapping community structures.

Statistical analysis of weighted networks

The relative perturbation norm of the weights as an index to assess the weight distribution is introduced and revealed new interesting statistical regularities in terms of the relative perturbedation norm useful for the statistical characterization of weighted graphs.

The Ubiquity of Small-World Networks

A new small-world metric, ω (omega), is proposed, which compares network clustering to an equivalent lattice network and path length to a random network, as Watts and Strogatz originally described.