path

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a path is a sequence of distinct nodes $x_1,x₂,…$ such that:

any 2 sucessive elements are joined by a link
no node is visited twice (said in distinct, but it is important and easy to overlook) with exception being that the start and end node can be the same. when they do be the same node, the path would be a cycle

Related conceptws

length of path

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network structures

In a network, there may be:

path
cycle, a specific type of pat
clique, a fully connected subnet
component, a connected subnet
k-kernel, a connected subnet where all node have at least k

length of path

nubmer of links in the path.

cycle

a cycle is a finite path \(x_1,x_2,...x_p\) such that \(x_1 =x_p\)

2 nodes in a network are connected if there exists a path in the network such that they are both member of it.

a network is connected if any pair of 2 nodes are connected by a path

If a network is not connected, then it could be split to connected compoenents

Author: Linfeng He

Created: 2024-04-03 Wed 20:58