' What is the betweenness of node mary in the network below? A .…

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' What is the betweenness of node mary in the network below?   A .…

Manu · Accepted Answer

Step 1: Identify All Pairs of Nodes First, list all pairs of nodes for which you will consider the shortest paths. In this network, the pairs are: Sarah and John Peter and John Sarah and Peter Explanation: List all possible pairs of nodes to find the shortest paths connecting them. Step 2: Determine Shortest Paths Between Each Pair For each pair of nodes, identify all shortest paths. Given the connections: Sarah--John : The shortest path can only be Sarah → Mary → John because there is no direct connection between Sarah and John. Peter--John : The shortest path can only be Peter → Mary → John because there is no direct connection between Peter and John. Sarah--Peter : The shortest path is direct, Sarah → Peter. Explanation: For each pair, identify the shortest routes connecting the nodes directly or via an intermediary. Step 3: Identify Paths That Pass Through Mary Next, identify which of these shortest paths pass through the node "Mary": Sarah to John : The path is Sarah → Mary → John. This path includes Mary. Peter to John : The path is Peter → Mary → John. This path includes Mary. Sarah to Peter : The path is Sarah → Peter. This path does not include Mary. Explanation: Identify the number of shortest paths that pass through the node "Mary." Step 4: Count the Number of Shortest Paths Through Mary From the paths listed: Paths through Mary: 2 (Sarah to John, Peter to John) Explanation: Count the number of shortest paths Step 5: Calculate Betweenness The betweenness centrality for a node is calculated as the number of shortest paths through the node divided by the total number of shortest paths. Here: Total number of shortest paths (considered for pairs involving Mary as a middle node): 3 (Sarah to John, Peter to John, Sarah to Peter) Number of these paths that pass through Mary: 2 Betweenness centrality of Mary = Number of paths through Mary Total number of paths = 2 3 Betweenness centrality of Mary = Total pairs Paths through Mary ​ = 3 2 Explanation: Divide the number of paths passing through Mary by the total number of shortest paths to get her betweenness centrality value. Final Answer: Option C. (2/3) is correct because two out of the three pairs' shortest paths pass through Mary.

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