Neighborhood Connectivity

The set of neighbors of a given node n is the node’s neighborhood and the number of its neighbors is its connectivity. The neighborhood connectivity of the node n is defined as the average connectivity of all the nearest neighbors of n (Maslov and Sneppen, 2002). Neighborhood connectivity is given by,

where, P (qk) is the conditional probability that a link belonging to a node with connectivity k points to a node with connectivity q. While C_N(k) obeys power law in the case of a hierarchical network, C_N(k) ∼ k^–β with β ∼ 0.5, for a scale-free network, C_N(k) ∼ constant (Pastor-Satorras et al., 2001; Malik et al., 2017). Positive and negative power dependence of C_N(k) could be the indicators of assortativity and disassortativity in the network topology, respectively (Barrat et al., 2004), meaning that if C_N(k) follows power-law with a positive value of exponent β (i.e., C_N(k) ∼ k^+β) then edges between highly connected nodes prevail in a network, this shows assortative nature of the network, whereas, if C_N(k) follows power-law with a negative value of exponent β (i.e., C_N(k) ∼ k^–β) then edges between lowly connected and highly connected nodes prevail in a network, this shows disassortative nature of the network.