# An Efficient Updation Approach for Enumerating Maximal (Δ, γ)Cliques of a Temporal Network

Given a temporal network 𝒢(𝒱, ℰ, 𝒯), (𝒳,[t_a,t_b]) (where 𝒳⊆𝒱(𝒢) and [t_a,t_b] ⊆𝒯) is said to be a (Δ, γ)clique of 𝒢, if for every pair of vertices in 𝒳, there must exist at least γ links in each Δ duration within the time interval [t_a,t_b]. Enumerating such maximal cliques is an important problem in temporal network analysis, as it reveals contact pattern among the nodes of 𝒢. In this paper, we study the maximal (Δ, γ)clique enumeration problem in online setting; i.e.; the entire link set of the network is not known in advance, and the links are coming as a batch in an iterative manner. Suppose, the link set till time stamp T_1 (i.e., ℰ^T_1), and its corresponding (Δ, γ)-clique set are known. In the next batch (till time T_2), a new set of links (denoted as ℰ^(T_1,T_2]) is arrived.

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