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Networks are collections of objects (*nodes* or *vertices*) and pairwise relations (ties or edges) between them. Formally, a graph *G* is a mathematical object composed of two sets: the vertex set *V* = {1,…, *n*} lists the nodes in the graph and the edge set *E* = {(*i, j*) : *i* ∼ *j*} lists all of the pairwise connections among the nodes. Here ∼ defines the relationship between nodes. The set *E* can encode binary or weighted relationships and directed or undirected relationships. A common and more concise representation of a network is given by the *n* × *n* adjacency matrix *A*, where entry *a _{ij}
* represents the directed relationship from object

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