The so-called y-structure Q holds all maximal cliques of active members at any time and every maximal clique is contained only once (y-structure invariant), where maximality refers only to the set of active semi-squares and not necessarily to the set of all semi-squares.
Therefore, the maximal clique is an induced subgraph of (G_v^-).
A maximal clique is a clique that is not a subset of any other clique in a community network [36].
The definition of a maximal clique is as follows: A maximal clique in a graph G is a clique not contained by any other clique in G.
A maximal clique is a clique (i.e. a complete subgraph) which is not a subset of any other clique in a network.
If we consider k, m, n > 2, then since we do not have any edges in the graph, the number of vertices in maximal clique is one.
As a result, the maximal clique is an induced subgraph of (G_u), which consists of vertex u and its neighboring vertices.
A maximal clique is perhaps the most fundamental dense substructure in a graph, and MCE is an important tool to discover densely connected subgraphs, with numerous applications to data mining on web graphs, social networks, and biological networks.
Moreover, there are graphs with exponentially many large cliques [34], and Algorithm 1 requires to list all and choose one at random (this is done to avoid starvation of cliques not listed first when one maximal clique is sought).
The authors show that a graph G is an edge clique graph if and only if it has a 2-labeling that satisfies the following two properties: (i) every maximal clique is strongly triangular and (ii) every strongly triangular set is a clique.
