the spread of disease and min cut figure contains pictorial representation of weighted graph generated by the centers for disease control (cdcin the course of studying an outbreak of tuberculosis in the united states each node represents personand each node is labeled by color indicating whether the person has active tbtested positive for exposure to tb ( high tst reaction rate)tested negative for exposure to tbor had not been tested the edges represent contact between pairs of people the weightswhich are not visible in the pictureindicate whether the contact between people was "closeor "casual figure spread of tuberculosis there are many interesting questions that can be formalized using this graph for exampleis it possible that all cases stemmed from single "indexpatientmore formallyis there nodensuch that there is path from to every other node in the graph with an active tb label? the answer is "almost there is path from the node in the middle of the graph to each active tb node except those nodes in the black circle on the right interestinglysubsequent investigation revealed that the person in the center of the black circle had previously been neighbor of the putative index patientand therefore there should have been casual contact edge linking the two to see color version of this graphgo to page of the edges of the graph do not capture anything related to time thereforethe existence of such node does not mean that the node represents an index patient howeverthe absence of such node would indicate the absence of an index patient we have necessarybut not sufficientcondition