# Assortative mixing in networks.

@article{Newman2002AssortativeMI, title={Assortative mixing in networks.}, author={Mark E. J. Newman}, journal={Physical review letters}, year={2002}, volume={89 20}, pages={ 208701 } }

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. Here we measure mixing patterns in a variety of networks and find that social networks are mostly assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortatively mixed network, which we study both analytically and numerically. Within this model we find that networks…

## 4,202 Citations

### Why social networks are different from other types of networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

It is demonstrated that group structure in networks can also account for degree correlations and that the predicted level of assortative mixing compares well with that observed in real-world networks.

### Assortativity of links in directed networks

- Computer Science, Business
- 2012

The overall assortativity of a network may be due to the number of assortative or disassortative links it has, the strength of such links, or a combination of both factors, which may be reinforcing or opposing each other.

### Assortative mixing in directed biological networks

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2012

Many biological networks, which have been previously classified as disassortative, are shown to be assortative with respect to these new measures.

### Assortative model for social networks.

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

A version of a network growth model, generalized in order to describe the behavior of social networks, one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure.

### Second-Order Assortative Mixing in Social Networks

- Computer Science
- 2017

It is concluded that second-order assortative mixing is a new property of social networks that suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same.

### Classifying Complex Networks using Unbiased Local Assortativity

- Computer ScienceALIFE
- 2010

It is demonstrated that the formulation proposed for local assortativity in Piraveenan et al. (2008) has a bias, which favours low-degree nodes over hubs, which needs to be removed before networks can be analysed in terms of local Assortativity.

### Robustness of networks with assortative dependence groups

- Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2018

## References

SHOWING 1-10 OF 59 REFERENCES

### Network robustness and fragility: percolation on random graphs.

- MathematicsPhysical review letters
- 2000

This paper studies percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolators, bond percolations, and models in which occupation probabilities depend on vertex degree.

### Emergence of scaling in random networks

- Computer ScienceScience
- 1999

A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

### Attack vulnerability of complex networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed.

### Immunization of complex networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

It is shown that the random uniform immunization of individuals does not lead to the eradication of infections in all complex networks, and networks with scale-free properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals.

### Resilience of the internet to random breakdowns

- Computer SciencePhysical review letters
- 2000

This work shows analytically and numerically that for alpha</=3 the transition never takes place, unless the network is finite, and finds that the physical structure of the Internet is impressively robust, with p(c)>0.99.

### Evolution of networks

- Computer Science
- 2002

The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.

### The structure of scientific collaboration networks.

- PhysicsProceedings of the National Academy of Sciences of the United States of America
- 2001

It is shown that these collaboration networks form "small worlds," in which randomly chosen pairs of scientists are typically separated by only a short path of intermediate acquaintances.

### Classes of small-world networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2000

Evidence of the occurrence of three classes of small-world networks, characterized by a vertex connectivity distribution that decays as a power law law, and the nature of such constraints may be the controlling factor for the emergence of different classes of networks are presented.

### Collective dynamics of ‘small-world’ networks

- Computer ScienceNature
- 1998

Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.

### Structure of growing networks with preferential linking.

- MathematicsPhysical review letters
- 2000

The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites and it is shown that the relation beta(gamma-1) = 1 between the exponents is universal.