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Structural Connectivity [1]

  • ε-Neighborhood:

\[ N_{\varepsilon }(v)=\left \{ w\epsilon \tau (v)|\sigma (v,w)\geq \varepsilon \right \} \]

  • Core:

\[CORE_{\varepsilon,\mu  }(v)\Leftrightarrow |N_{\varepsilon } (v)|\geq \mu \]

  • Direct structure reachable:

\[DirRECH_{\varepsilon,\mu  }(v,w)\Leftrightarrow CORE_{\varepsilon,\mu  }(v)\wedge w\epsilon N_{\varepsilon } (v)\]

  • Structure reachable: transitive closure of direct structure reachability
  • Structure connected:

\[CONNECT_{\varepsilon,\mu  }(v,w)\Leftrightarrow \exists u\epsilon V:RECH_{\varepsilon,\mu  }(u,v)\wedge RECH_{\varepsilon,\mu  }(u,w)\]

Speaker notes:

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M. Ester, H. P. Kriegel, J. Sander, & X. Xu (KDD'96) “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases