Question

Consider a neural network with a finite number of nodes, where there is a connection between any pair of nodes. Moreover, each connection has a direction, so that signals can travel in that direction, but not the other. (In other words, we have a complete graph and each edge comes with an ordering of its two vertices.) Show that there is a node that can send signals to any other node, either directly, or via one intermediate node.

          Consider a neural network with a finite number of nodes, where there is a connection between any pair of nodes. Moreover, each connection has
a direction, so that signals can travel in that direction, but not the other. (In other words, we have a complete graph and each edge comes with
an ordering of its two vertices.) Show that there is a node that can send signals to any other node, either directly, or via one intermediate node.

Consider a neural network with a finite number of nodes, where there is a connection between any pair of nodes. Moreover, each connection has
a direction, so that signals can travel in that direction, but not the other. (In other words, we have a complete graph and each edge comes with
an ordering of its two vertices.) Show that there is a node that can send signals to any other node, either directly, or via one intermediate node.

Added by Mitchell A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Stephen Zaffke

Step 1

We can draw the connections between these nodes as follows: A -> B B -> C C -> A In this case, we can see that node A can send signals directly to node B, and node B can send signals directly to node C. However, node A cannot send signals directly to node C. Show more…

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That is all just directions matters. Consider a neural network with a finite number of nodes, where there is a connection between any pair of nodes. Moreover, each connection has a direction, so that signals can travel in that direction, but not the other. (In other words, we have a complete graph and each edge comes with an ordering of its two vertices.) Show that there is a node that can send signals to any other node, either directly or via one intermediate node.