Finding the mother vertex in a graph

Networks or graphs are pivotal in so many real-world applications such as fraud prevention systems. search engines, recommendation systems, social networks and a lot more. The search for the mother vertex of a graph aids in understanding the accessibility of a given vertex or collection of vertices. 

What is the meaning of the mother vertex in a given graph?

In a given graph G = (V, E), a mother vertex v has a pathway for all other vertices in the specified graph to enable the connection. All other vertices in the graph can be accessed via the mother vertex. A mother vertex is quite common in directed graphs but is also applicable in undirected networks. We will briefly explore mother vertices in different network examples

Directed graph: Directed graphs or DiGraphs do hold directed edges or nodes. These edges can be unidirectional or bidirectional. For DiGraphs, self-loops are permissible but parallel edges are not. Mother vertex exists in directed graphs and there can be multiple of these as shown below.  Based on the directed graph below, nodes [4] and [6] are the mother vertex. 

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