The higher level sub-network is a path visiting two or more nodes.
37. A Hamiltonian path on a graph is a path visiting every node exactly once.
After having the Euclidean distance, the ME tour path visits only some specific nodes to minimize the tour length.
In this study, a cycle of length l is defined as a path visiting a node twice and visiting other l−2 nodes exactly once.
Fig. 2 The diagram of the besieged walker, where a shows the walker is besieged by the path visited before, b shows the walker is besieged by sensors.
You even end up taking the road less traveled and find yourself off the beaten path, visiting more than just the typical travel sites of your new turf.
Note also that each path visits the nodes in increasing order of indices j.
Similarly, we have σ(A∪{u})−σ(A)≥σ(B∪{u})−σ(B) because σ(A∪{u})−σ(A) is the sum of probabilities of simple paths visit u exactly once in community (A∪{u}), and σ(B∪{u})−σ(B) is the sum of probabilities of simple paths visit u exactly once in community (B∪{u}) which is a subset of the former.
