Abstract
Graphs describe and represent many complex structures in the field of social networks, biological, chemical, industrial and transport systems, and others. These graphs are not only connected but often also k-connected (or at least part of them). Different metrics are used to determine the distance between two nodes in the graph. In this article, we propose a novel metric that takes into account the higher degree of connectivity on the part of the graph (for example, biconnected fullerene graphs and fulleroids). Designed metric reflects the cyclical interdependencies among the nodes of the graph. Moreover, a new component model is derived, and the examples of various types of graphs are presented.
Highlights
More interconnected parts of graphs play an essential role in the social and natural sciences
We focus on generalizing biconnected components of a graph and we define a novel metric that considers higher degree of connectivity on the part of the graph
The paper [34] contains a method for community detection based on network decomposition
Summary
More interconnected parts of graphs play an essential role in the social and natural sciences. Our approach is based on the cycle length limit in the definition of biconnected components. The distance between two vertices in the graph is defined as the length of the shortest closed trail that contains these two vertices. We define a new measure on an undirected connected graph without bridges for the measurement of distances using cyclic subgraphs.
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