Cumulative Contact Probability (CCP)
Cumulative Contact Probability
(CCP) was introduced by Gao et al. [2] as a centrality-based heuristic for the Single-Data Multicast (SDM) problem, which seeks to determine how to select the minimum number of relays required to achieve a target delivery ratio \(p\) within a time constraint \(T\) when delivering a data item to a set \(D\) of destinations. The CCP measure is derived from a Poisson model of contact processes in social networks. The centrality of node \(i\), denoted by \(c_{\text{CCP}}(i)\), is defined as
\begin{equation*}
c_{\text{CCP}}(i) = 1 - \frac{1}{N-1} \sum_{j=1}^{N} e^{-λ_{ij} T},
\end{equation*}
where \(λ_{ij}\) represents the contact rate between nodes \(i\) and \(j\). In unweighted networks, the contact rate \(λ_{ij}\) reduces to a binary indicator of link existence, that is, \(λ_{ij} = a_{ij}\), where \(A = [a_{ij}]\) denotes the adjacency matrix of the network. Hence, the CCP index quantifies the average probability that a randomly chosen node in the network is contacted by node \(i\) within the time interval \(T\).