English

Ordered community structure in networks

Physics and Society 2012-02-15 v3 Social and Information Networks

Abstract

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have discrete values, but many networks exhibit assortative mixing by some continuous-valued attribute, such as age or geographical location. In such cases, no discrete communities can be identified. We consider how the notion of community structure can be generalized to networks that are based on continuous-valued attributes: in general, a network may contain discrete communities which are ordered according to their attribute values. We propose a method of generating synthetic ordered networks and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.

Keywords

Cite

@article{arxiv.1104.0923,
  title  = {Ordered community structure in networks},
  author = {Steve Gregory},
  journal= {arXiv preprint arXiv:1104.0923},
  year   = {2012}
}

Comments

This is an extended preprint version that includes an extra example: the college football network as an ordered (spatial) network. Further improvements, not included here, appear in the journal version. Original title changed (from "Ordered and continuous community structure in networks") to match journal version

R2 v1 2026-06-21T17:49:53.662Z