Abstract
A fundamental organizing principle of real-world complex networked systems is modularity, where networks have interactions at different levels. In this paper we consider a modular graph G having modules with arbitrary intraconnections and random interconnections between activated vertices in different modules. The vertices in different modules are activated with probability r and linked by an interconnecting edge with probability p independently. We present results regarding the Cheeger constant, robustness, algebraic connectivity as well as the smallest eigenvalue for the Dirichlet Laplacian matrix of G with high probability. Our results suggest that r=(lnn)/n is a potential scaling for the recently observed external field-like phenomena of modular networks in statistical mechanics.
Original language | English |
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Pages (from-to) | 135-144 |
Number of pages | 10 |
Journal | Discrete Applied Mathematics |
Volume | 338 |
Early online date | 17 Jun 2023 |
DOIs | |
Publication status | Published - 1 Oct 2023 |
Keywords
- Cheeger constant
- Laplacian spectrum
- Modular graph
- Random graph