# Analysis of weighted networks.

@article{Newman2004AnalysisOW, title={Analysis of weighted networks.}, author={Mark E. J. Newman}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2004}, volume={70 5 Pt 2}, pages={ 056131 } }

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph…

## 2,140 Citations

### Node centrality in weighted networks: Generalizing degree and shortest paths

- Computer ScienceSoc. Networks
- 2010

### Basic Notions for the Analysis of Large Affiliation Networks / Bipartite Graphs

- Computer Science
- 2006

This work proposes an extension of the most basic notions used nowadays to analyse classical complex networks to the bipartite case, and introduces a set of simple statistics, which are discussed by comparing their values on a representative set of real-world networks and on their random versions.

### Weighted networks: the issue of dichotomization

- Computer ScienceInternational Journal of Tourism Sciences
- 2019

It is concluded that while unweighted networks can provide insights into some structural properties, the operation can be unnecessary and even detrimental for studying many features and processes when valued relational data are available.

### On the rich-club effect in dense and weighted networks

- Computer Science
- 2009

This work focuses on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient, and represents a generalization of the richest network to weighted networks which is complementary to other recently proposed ones.

### Analysing Weighted Networks: An Approach via Maximum Flows

- Computer ScienceComplex
- 2009

We present an approach for analysing weighted networks based on maximum flows between nodes and generalize to weighted networks ‘global’ measures that are well-established for binary networks, such…

### Sampling algorithms for weighted networks

- Computer ScienceSocial Network Analysis and Mining
- 2016

This paper proposes that when the network model is chosen to be a weighted network, then the network measures such as degree centrality, clustering coefficient and eigenvector centrality must be redefined and new network sampling algorithms must be designed to take the weights of the edges of the network into consideration.

### Persistent Homology of Collaboration Networks

- Computer Science
- 2013

Persistent homology, a recent technique from computational topology, is used to analyse four weighted collaboration networks and it is shown that persistent homology corresponds to tangible features of the networks.

### Detecting degree symmetries in networks.

- Mathematics, Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

It is found that most studied examples of degree symmetry are weakly positively degree symmetric, and the exceptions are an airport network (having a negative degree-symmetry coefficient) and one-mode projections of social affiliation networks that are rather strongly degree asymmetric.

### Statistical properties of weighted complex networks characterized by metaweights

- Computer Science
- 2010

## References

SHOWING 1-10 OF 54 REFERENCES

### Finding and evaluating community structure in networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

It is demonstrated that the algorithms proposed are highly effective at discovering community structure in both computer-generated and real-world network data, and can be used to shed light on the sometimes dauntingly complex structure of networked systems.

### The architecture of complex weighted networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2004

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.

### Community structure in social and biological networks

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2002

This article proposes a method for detecting communities, built around the idea of using centrality indices to find community boundaries, and tests it on computer-generated and real-world graphs whose community structure is already known and finds that the method detects this known structure with high sensitivity and reliability.

### Fast algorithm for detecting community structure in networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

An algorithm is described which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster, than previous algorithms.

### Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is argued that simple networks such as these cannot capture variation in the strength of collaborative ties and proposed a measure of collaboration strength based on the number of papers coauthored by pairs of scientists, and thenumber of other scientists with whom they coauthored those papers.

### Workshop on Algorithms and Models for the Web Graph

- Computer ScienceWAW
- 2006

This study has made a significant impact on research in physics, computer science and mathematics and given birth to new branches of research in different areas of mathematics, most notably graph theory and probability.

### Weighted evolving networks.

- Computer SciencePhysical review letters
- 2001

This paper introduces and investigates the scaling properties of a class of models which assign weights to the links as the network evolves, and indicates that asymptotically the total weight distribution converges to the scaling behavior of the connectivity distribution, but this convergence is hampered by strong logarithmic corrections.

### Defining and identifying communities in networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2004

This article proposes a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability and applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods.

### Detecting network communities: a new systematic and efficient algorithm

- Computer Science
- 2004

An efficient and relatively fast algorithm for the detection of communities in complex networks is introduced. The method exploits spectral properties of the graph Laplacian matrix combined with…