Unevenness of Loop Location in Complex Networks

Abstract

The loop structure plays an important role in many aspects of complex networks and attracts much attention. Among the previous works, Bianconi et al find that real networks often have fewer short loops as compared to random models. In this paper, we focus on the uneven location of loops which makes some parts of the network rich while some other parts sparse in loops. We propose a node removing process to analyze the unevenness and find rich loop cores can exist in many real networks such as neural networks and food web networks. Finally, an index is presented to quantify the unevenness of loop location in complex networks.

7 pages, 6 figures

References in corpus (13)

• Synchronization in complex networks
• Critical phenomena in complex networks
• Prominence and control: The weighted rich-club effect
• Cycles and clustering in bipartite networks
• Local structure of directed networks
• Random acyclic networks
• Algorithm for counting large directed loops
• An algorithm for counting circuits: application to real-world and random graphs
• Optimal Tree for Both Synchronizability and Converging Time
• Ranking by Loops: a new approach to categorization
• Statistics of cycles in large networks
• Finding long cycles in graphs
• Percolation and Loop Statistics in Complex Networks

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