[...] (Latora and Marchiori, 2004). The network efficiency E(G) is a measure to quantify how efficiently the nodes of a network exchange information. To define efficiency of a network G, first we calculate the shortest path lengths between the ith and the jth nodes. Let us now suppose that every node sends information along the network, through its links. The efficiency in the communication between the ith node and the jth node is inversely proportional to the shortest distance: when there is no path in the graph between the ith and the jth nodes, we get and efficiency becomes zero. Let N be known as the size of the network or the numbers of nodes in the graph, the average efficiency of the graph (network) of G can be defined as:
The above formula gives a value of in the interval of [0, 1].
2. The efficiency of a network
The network efficiencyE, is a measure introduced in Refs. [5,6] to quantify how efficiently the nodes of the network exchange information.
To define the efficiency of G first we have to calculate the shortest path lengths between two generic points i and j.
Let us now suppose that every vertex sends information along the network, through its edges. We assume that the efficiency in the communication between vertex i and j is inversely proportional to the shortest distance: [...] when there is no path in the graph between i and j we get consistently Consequently the average efficiency of the graph G can be defined as :
Such a formula (1) gives a value of E that can vary in the range ,
Though the source is given, there is no hint that the text following the reference is taken nearly word-for-word from the source (with some shortening). Also, it makes no sense to speak of the "ith" and "jth" node as there is no linear order on a graph. The nodes are just referred to as "i" and "j", as in the source.
At the end, Nm produces a mathematical mistake by leaving out too much.