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Networks Basic Statistics

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Objectives

  • Compute the degree distribution for undirected and directed networks
  • Quantify the local density of connectivity in the network
  • Understand why motif distributions must be estimated in large networks

Introduction

Fundamentally, a network is a body of data. As with other data sets, our first task it to identify significant features of that data. In much the same way as the mean and standard deviation are easy to compute but very valuable summary statistics, degree, clustering, and motif statistics are easy to compute attributes that can reveal a great deal about the structure of a network. We discuss these different basic statistics here.

Degree Distribution

Out and In Degrees

Scale-free Distributions

Clustering Coefficient

Transitive Triples

Motif Distributions

Conclusion

References

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Discussion questions

Problems

Glossary

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