The H0H0 function, a new index for detecting structural/topological complexity information in undirected graphs

• New index to measure the complexity of connected undirected graphs.
• Lowest zero value with an infinite chain of nodes.
• Highest two value with an infinite number of nodes full connected.
• New algorithm to determine graph similarity, also with different number of nodes.
• Different levels of similarity: normal, weak and strong.

Significant applications such as the analysis of Alzheimer’s disease differentiated from dementia, or in data mining of social media, or in extracting information of drug cartel structural composition, are often modeled as graphs. The structural or topological complexity or lack of it in a graph is quite often useful in understanding and more importantly, resolving the problem. We are proposing a new index we call the H0H0function   to measure the structural/topological complexity of a graph. To do this, we introduce the concept of graph pruning and its associated algorithm that is used in the development of our measure. We illustrate the behavior of our measure, the H0H0 function, through different examples found in the appendix. These examples indicate that the H0H0 function contains information that is useful and important characteristics of a graph. Here, we restrict ourselves to undirected.