Network Marketing is a business tool that builds a network of business partners or distributors by directly selling products and services through a word-of-mouth marketing strategy. NM graph is a graphical representation of the network marketing industry. Just like a graph consists of vertices and edges, network marketing consists of distributors/ business partners which represent the vertices of the NM graph, and edges determine the genealogy of the network. In this paper, we explore the structure of an NM graph by graph parameters and see how the graph reflects various properties of a network of people. It is seen that an NM graph is a rooted binary tree. The measure of the influence of a network and the measure of profitability of a network is determined. It is seen that the objective to maximize profit by allocating different stakes to different persons is a typical case of an assignment problem. The genealogy of a network can be determined by studying the adjacency matrix of the NM digraph. Graph parameter like eccentricity represents the strongest person in the network earning maximum profitability. The domination number acts as a measure of the stability of an NM graph.
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