page_title: Cederbaum's maximum flow theorem
section_title: iv characteristic
hierarchical_section_title: Cederbaum's maximum flow theorem / Definitions / iv characteristic
caption_attribution_description: English: iv characteristic for resistive electrical network
context_page_description: Cederbaum's theorem defines hypothetical analog electrical networks which will automatically produce a solution to the minimum s–t cut problem. Alternatively, simulation of such a network will also produce a solution to the minimum s–t cut problem. The presentation in this article closely follows the presentation of the theorem in the original publication.
context_section_description: The  characteristic is the relationship between current and voltage.  The requirements are:
  (i)   Current and voltage are continuous function with respect to one another. 
  
  (ii)  Current and voltage are non-decreasing functions with respect to one another. 
  
  (iii) The range  of the current is limited by the weights of the forward and reverse edges corresponding to the resistive element.  The current range may be inclusive or exclusive of the endpoints.  The domain of the voltage is exclusive of the maximum and minimum currents:
   iab :  R → [−wab,wba]   or   (−wab,wba]   or  [−wab,wba)   or  (−wab,wba)
   vab :  (−wab,wba)  →  R
caption: i
          v
        
      
      {\displaystyle iv}
    
   characteristic.
exif: {}