Document Type : Original Article


1 Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Faculty of Computer Science and Engineering, Shahid Beheshti University, Tehran, Iran


Over the past few years, the study of complex networks as an interdisciplinary subject has yielded numerous insights. Communication links within these networks have been found to play a crucial role in shaping the implementation of dynamic processes. Recursive graphs are a class of complex networks whose internal structure is governed by recurrent relations. Among these, line graphs are especially important because they represent the communication links within the network as nodes. Studying the heterogeneity, or irregularity, of different graph models is a fundamental research issue in complex and social network analysis. In this article, we investigate the mapping between graph robustness and heterogeneity metrics and their equivalent metrics in line graphs. Specifically, we analyze the distribution of eigenvalues and important indices of heterogeneity in recursive and line graphs. We also examine the changes in heterogeneity of recursive line graphs with the introduction of a set of important heterogeneity indices. Our approach is broadly applicable to a wide range of indicators and complex networks beyond those discussed in this study.


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