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When we model an opportunistic network using a periodic graph, each node in the static graph, (i in mathcal {V}) represents a person or a sensor node.
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In this subsection, we will use a periodic graph shown in Fig. 2 to explain our algorithm given in this section.
A Bayesian procedure for analyzing longitudinal binary responses using a periodic cosine function was developed.
It is also possible to cluster a periodic graph using the betweenness centrality of its static graph.
Also, we define a period of a periodic graph G as follows: (Period of Periodic Graph) Let (mathcal {G} = (mathcal {V}, mathcal {E}, mathrm {w})) be a static graph of a 1-dimensional periodic graph G. Let (mathcal {E} = {e^{(1)}, dots, e^{(|mathcal {E}|)}}) and, for all (e^{(t)}), (e^{(t)} = (i^{(t)}, j^{(t)}, langle g^{(t)} rangle )).
We do not give an algorithm for a general 1-dimensional one periodic graph, but a periodic graph used for capturing behaviors of an opportunistic network.
A periodic graph is an infinite repetition of a finite structure.
Start out with an abstract formulation of a periodic graph, i.e., a set of vertices and a set of edges.
Recall that a periodic graph contains a repetitive structure, and each part corresponds to a snapshot at time h.
In a periodic graph generated by the static graph, there are infinite copies of the node i, ((i, langle h rangle )) for (h in mathbb {Z}).
As the number of nodes of an periodic graph is infinite, it is not clear if we can directly use the definition in our setting.
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