Volume entropy, weighted girths and stable balls on graphs

Florent Balacheff*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


We prove new isoperimetric inequalities on graphs involving quantities linked with concepts from differential geometry. First, we bound from above the product of the volume entropy (defined as the log of the exponential growth rate of the universal cover) and the girth of weighted graphs in terms of their cyclomatic number. In a second part, we study a natural polyhedron associated to a weighted graph: the stable ball. In particular, we relate the volume of this polyhedron, the weight of the graph nd its cyclomatic number.

Original languageEnglish
Pages (from-to)291-305
Number of pages15
JournalJournal of Graph Theory
Issue number4
Publication statusPublished - Aug 2007


  • Girth
  • Stable norm
  • Systole
  • Volume entropy


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