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Illustrations of cliques, simplices, holes, and clique complex. The simplices are shaded for identification. (A) 3 and 4-cliques, which are associated to 2 and 3-dimensional simplices. (B) a 1-dimensional hole, or cycle, is a closed path of edges of length greater than 3. (C) Combining the elements of (A,B) following the rules in Section 2.2.1, one can produce a clique complex with one 1-dimensional hole. All simplices in this figure are shaded as is customary.
