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Overlapping community detection . Overlapping. Overlapping means that some vertices may belong to more than one community. agglomerativ E hierarchic A l clusterin G based on maxima L cliqu E.

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## Overlapping community detection

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**Overlapping**• Overlapping means that some vertices may belong to more than one community.**agglomerativEhierarchicAlclusterinG based on maximaLcliquE**• EAGLE algorithm is presented to uncover both the overlapping and hierarchical community structures of networks. • EAGLE algorithm has two stages: • 1. A dendrogram is generated. • 2. We choose an appropriate cut which breaks the dendrogram into communities.**The first stage**• 1.Find out all maximal cliques in the network(Bron-Kerbosch algorithm).Note that not all maximal cliques are taken into account.Weset a threshold k and neglecting all the maximal cliques with the size smaller than k. k=4 k=3**2.Select the pair of communities with the maximum**similarity,incorporate them into a new one and calculate the similarity between the new community and other communities. C1, C2 :community1,2 k:the degree of the vertex A:the adjacency matrix of the network m:the total number of edges in the network**3.Repeat step 2 until only one community remains.**Stage 2: • The task of the second stage of the algorithm EAGLE is to cut the dendrogram. • Ov:the number of communities to which vertex v belongs.**Step1:every vertex is given a unique label. After few**iterations the label of vertex is the set of pairs (c,b). c: community identifier b: belong coefficient Ex. The label of vertex x={(1,0.2),(2,0.3),(3,0.5)}**Step2:each vertex x updates its label by replacing it by the**label used by the greatest number of neighbours.**Step3: if the algorithm satisfies the stop criterion , the**algorithm stop.**Threshold:1/v**V:the maximum number of communities to which any vertex can belong. Ex.threshold=1/2 • Ex. (e,1) (b,1) e b (f,1/3) (g,1/3) (a,1/3) (f,1) c f (c,1/3) (d,1/3) (a,1/3) a (c,1) (a,1) d g (g,1) (d,1) (initialize) (d,1/4) (b,1/4) (e,1/4) (g,1/4) (e,1/3) (f,1/3) (a,1/3) (c,1/3) (b,1/3) (a,1/3) (first iteration)**(c,1/3)**(e,1/3) (b,1/6) (d,1/6) (e,5/6) (g,1/6) (g,1/6) (f,1/3) (e,3/6) (c,2/4) (f,1/4) (e,1/4) (third iteration) (c,1/3) (e,1/3) (b,1/6) (d,1/6) (second iteration)

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