That's an X-ray of a very worried person. This is Kenzo. Kenzo is very worried about his research future in the graphs field. So worried that the doctors could see a graph of his thoughts! Seizing the opportunity, the doctors were also a great admirer of graphs and said to Kenzo:
- "I have the results of your brain exams, Kenzo...I have news... a good and a not so good one. Which of them you want me to tell first?"
- "The good one first, please..."
- "The good one is that we found a graph in your brain that we could solve it and have some fun!"
- "That sounds okay..! So what would be the other one then?"
- "This graph helped us to find a tumor in your brain! (😃)"
- "... a tumor?"
- "...Yes, a tumor."
- "(😐)"
- "(😅)"
Below we have Kenzo's brain graph. Considering the weights here helped the doctor to find the tumor, then the weights represents intensity or abnormal activity levels. Which of the statements the doctor and Kenzo conclude are true?
I. The graph is directed, weighted and its adjacency matrix has order 6, its last element is 0, it has one strongly connected component, the trace of the adjacency matrix is 0 and the total degree is equal to 68.3 ;
II. The graph is directed, weighted and the adjacency matrix is squared, its last element is 0, it has two strongly connected component, the adjacency is symmetric and the total degree is equal to 68.3;
III. Nodes A and B are In-components and the tumor is in the node's E neighborhood;
IV. The element a_{35} = 1.3, that's a complete graph and the node D is a tumor;%3CmxGraphModel%3E%3Croot%3E%3CmxCell%20id%3D%220%22%2F%3E%3CmxCell%20id%3D%221%22%20parent%3D%220%22%2F%3E%3CmxCell%20id%3D%222%22%20value%3D%222%26lt%3Bspan%20style%3D%26quot%3Bcolor%3A%20rgba(0%2C%200%2C%200%2C%200)%3B%20font-family%3A%20monospace%3B%20font-size%3A%200px%3B%20text-align%3A%20start%3B%20text-wrap%3A%20nowrap%3B%26quot%3B%26gt%3B%253CmxGraphModel%253E%253Croot%253E%253CmxCell%2520id%253D%25220%2522%252F%253E%253CmxCell%2520id%253D%25221%2522%2520parent%253D%25220%2522%252F%253E%253CmxCell%2520id%253D%25222%2522%2520value%253D%25221%2522%2520style%253D%2522text%253Bhtml%253D1%253Balign%253Dcenter%253BverticalAlign%253Dmiddle%253BwhiteSpace%253Dwrap%253Brounded%253D0%253Brotation%253D-70%253B%2522%2520vertex%253D%25221%2522%2520parent%253D%25221%2522%253E%253CmxGeometry%2520x%253D%2522295%2522%2520y%253D%2522204.63%2522%2520width%253D%252260%2522%2520height%253D%252230%2522%2520as%253D%2522geometry%2522%252F%253E%253C%252FmxCell%253E%253C%252Froot%253E%253C%252FmxGraphModel%253E%26lt%3B%2Fspan%26gt%3B%26lt%3Bspan%20style%3D%26quot%3Bcolor%3A%20rgba(0%2C%200%2C%200%2C%200)%3B%20font-family%3A%20monospace%3B%20font-size%3A%200px%3B%20text-align%3A%20start%3B%20text-wrap%3A%20nowrap%3B%26quot%3B%26gt%3B%253CmxGraphModel%253E%253Croot%253E%253CmxCell%2520id%253D%25220%2522%252F%253E%253CmxCell%2520id%253D%25221%2522%2520parent%253D%25220%2522%252F%253E%253CmxCell%2520id%253D%25222%2522%2520value%253D%25221%2522%2520style%253D%2522text%253Bhtml%253D1%253Balign%253Dcenter%253BverticalAlign%253Dmiddle%253BwhiteSpace%253Dwrap%253Brounded%253D0%253Brotation%253D-70%253B%2522%2520vertex%253D%25221%2522%2520parent%253D%25221%2522%253E%253CmxGeometry%2520x%253D%2522295%2522%2520y%253D%2522204.63%2522%2520width%253D%252260%2522%2520height%253D%252230%2522%2520as%253D%2522geometry%2522%252F%253E%253C%252FmxCell%253E%253C%252Froot%253E%253C%252FmxGraphModel%253E%26lt%3B%2Fspan%26gt%3B%22%20style%3D%22text%3Bhtml%3D1%3Balign%3Dcenter%3BverticalAlign%3Dmiddle%3BwhiteSpace%3Dwrap%3Brounded%3D0%3Brotation%3D-10%3B%22%20vertex%3D%221%22%20parent%3D%221%22%3E%3CmxGeometry%20x%3D%22343.74%22%20y%3D%22160%22%20width%3D%2260%22%20height%3D%2230%22%20as%3D%22geometry%22%2F%3E%3C%2FmxCell%3E%3C%2Froot%3E%3C%2FmxGraphModel%3E
(A) I., III. and IV. are true.
Interesting question, but certain things are unclear. Total degrees are always integers, so I and II are false. It is not clear how tumors are defined. Apparently, it has to do with edge weights but a clear definition is needed. Finally, alternative (D) contains a 'maybe', so 'maybe' it is right. We need unambiguous alternatives.
ResponderExcluirHey, professor! Thank you for your comment! I disagree that all Total degrees are integer, in fact they fully depend on the networks weights, which in this exercise we considered a decimal number, and that's not wrong. I'll edit the alternative (D) and (E) :)
Excluir