A framework for the construction of generative models for mesoscale structure in multilayer networks

Bazzi, Marya; Jeub, Lucas G. S.; Arenas, Àlex; Howison, Sam; Porter, Mason A.

doi:10.1103/physrevresearch.2.023100

Cited by 33 publications

(42 citation statements)

References 106 publications

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“…As regards the generation of the multi-layer networks, we refer to the generative model in 16 . To the best of our knowledge, this provides the most general platform in the literature for generating synthetic multi-layer communities that takes into consideration different types of multi-layer networks.…”

Section: Methodsmentioning

confidence: 99%

“…At the third phase, a multi-layer edge generation model can be used to create edges of the multi-layer network given the implanted community assignments resulted from the previous step. In our experiments, we generate out synthetic networks using a variant of the degree-corrected SBM benchmark that avoid the creation of self-loops and parallel edges 16 . We chose to fix the mixing parameter in edge generation phase in our experiments to a very small value (µ = .…”

Section: Methodsmentioning

confidence: 99%

“…Despite the variety of existing generative models for multi-layer communities in multi-layer networks 16,[23][24][25][26][27][28][29][30][31] , they focus on a limited amount of structures for multi-layer communities, or produce multi-layer communities that are not straightforwardly mappable to real-world scenarios in multi-layer networks. Here we hypothesize some real-world scenarios for multi-layer communities and interpret them into different multi-layer community models.…”

Section: Models For Multi-layer Communities In Multiplex and Time-depmentioning

confidence: 99%

“…Second, most multi-layer community detection methods are mathematical extensions of single-layer community discovery methods, which made it possible to provide such methods without having to investigate a precise extension of their original conceptualisations. From a structural perspective, recent work 16 argues that there are two primary differences between a single-layer community and a multi-layer one. First, a multi-layer community can expand over multiple layers.…”

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confidence: 99%

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Unspoken Assumptions in Multi-layer Modularity maximization

Hanteer

Magnani

2020

Sci Rep

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A principled approach to recover communities in social networks is to find a clustering of the network nodes into modules (i.e groups of nodes) for which the modularity over the network is maximal. This guarantees partitioning the network nodes into sparsely connected groups of densely connected nodes. A popular extension of modularity has been proposed in the literature so it applies to multi-layer networks, that is, networks that model different types/aspects of interactions among a set of actors. in this extension, a new parameter, the coupling strength ω, has been introduced to couple different copies (i.e nodes) of the same actor with specific weights across different layers. This allows two nodes that refer to the same actor to reward the modularity score with an amount proportional to ω when they appear in the same community. While this extension seems to provide an effective tool to detect communities in multi-layer networks, it is not always clear what kind of communities maximising the generalised modularity can identify in multi-layer networks and whether these communities are inclusive to all possible community structures possible to exist in multi-layer networks. in addition, it has not been thoroughly investigated yet how to interpret ω in real-world scenarios, and whether a proper tuning of ω, if exists, is enough to guarantee an accurate recoverability for different types of multi-layer community structures. In this article, we report the different ways used in the literature to tune ω. We analyse different community structures that can be recovered by maximising the generalised modularity in relation to ω. We propose different models for multi-layer communities in multiplex and time-dependent networks and test if they are recoverable by modularity-maximization community detection methods under any assignment of ω. Our main finding is that only few simple models of multi-layer communities in multiplex and time-dependent networks are recoverable by modularity maximisation methods while more complex models are not accurately recoverable under any assignment of ω. Community detection is one of the core tasks in the analysis of complex networks. It involves partitioning the network into groups of nodes, also known as communities, partitions, cohesive groups or clusters. The importance of this task comes from its ability to break large networks into smaller building blocks so it becomes easier to understand the structure of the network and the role played by each node. Applications of community detection algorithms are ubiquitous, including social media group detection 1 , thematic community detection 2 , second-order flow analysis in human mobility 3 , and topic detection in information networks 4. A community detection solution is usually represented as a clustering  where  = …

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Models For Multi-layer Communities In Multiplex and Time-depmentioning

confidence: 99%

mentioning

confidence: 99%

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Unspoken Assumptions in Multi-layer Modularity maximization

Hanteer

Magnani

2020

Sci Rep

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“…Second, to appropriately handle the null model in the multilayer modularity framework (see (1.2)), we have adapted the field term, \theta l t , to be layer-specific and to only contribute to the beliefs originating from nodes within a given layer, l. Having a separate null model for each layer is one of the differentiating features between the original modularity and multilayer modularity defined in (1.1). 3 Finally, we introduce an additional interlayer contribution, scaled by interlayer coupling parameter \omega , to account for interlayer edges in a manner similar to the interlayer contributions to multilayer modularity, leading to the new update equation,…”

Section: 2mentioning

confidence: 99%

Multilayer Modularity Belief Propagation to Assess Detectability of Community Structure

Weir¹,

Walker²,

Zdeborová³

et al. 2020

SIAM Journal on Mathematics of Data Science

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Modularity-based community detection encompasses a number of widely used, efficient heuristics for identification of structure in networks. Recently, a belief propagation approach to modularity optimization provided a useful guide for identifying nontrivial structure in single-layer networks in a way that other optimization heuristics have not. In this paper, we extend modularity belief propagation to multilayer networks. As part of this development, we also directly incorporate a resolution parameter. We show that adjusting the resolution parameter affects the convergence properties of the algorithm and yields different community structures than the baseline. We compare our approach with a widely used community detection tool, GenLouvain, across a range of synthetic, multilayer benchmark networks, demonstrating that our method performs comparably to the state of the art. Finally, we demonstrate the practical advantages of the additional information provided by our tool by way of two real-world network examples. We show how the convergence properties of the algorithm can be used in selecting the appropriate resolution and coupling parameters and how the node-level marginals provide an interpretation for the strength of attachment to the identified communities. We have released our tool as a Python package for convenient use.

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Generating large scale‐free networks with the Chung–Lu random graph model

2020

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Random graph models are a recurring tool‐of‐the‐trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test‐bed generators for studying diffusion and routing processes on networks. In this paper, we illustrate how to generate large random graphs having a power‐law degree distribution using the Chung–Lu model. In particular, we are concerned with the fulfillment of a fundamental hypothesis that must be placed on the model parameters, without which the generated graphs lose all the theoretical properties of the model, notably, the controllability of the expected node degrees and the absence of correlations between the degrees of two nodes joined by an edge. We provide explicit formulas for the model parameters to generate random graphs that have several desirable properties, including a power‐law degree distribution with any exponent larger than 2, a prescribed asymptotic behavior of the largest and average expected degrees, and the presence of a giant component.

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A framework for the construction of generative models for mesoscale structure in multilayer networks

Cited by 33 publications

References 106 publications

Unspoken Assumptions in Multi-layer Modularity maximization

Unspoken Assumptions in Multi-layer Modularity maximization

Multilayer Modularity Belief Propagation to Assess Detectability of Community Structure

Generating large scale‐free networks with the Chung–Lu random graph model

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