Generative model for reciprocity and community detection in networks

Safdari, Hadiseh; Contisciani, Martina; Bacco, Caterina De

doi:10.1103/physrevresearch.3.023209

Cited by 21 publications

(26 citation statements)

References 46 publications

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“…where η as a hyperparameter regulates the reciprocity effects, similarly as in [25]. The difference between Eq.…”

Section: Modelmentioning

confidence: 99%

“…The difference between Eq. 1 and the edge probability in [25] is that the dependency on the reciprocated tie is on the previous time step, while standard CRep considers only the same time t, being an approach valid for static networks. Furthermore, an edge could disappear with rate µ.…”

Section: Modelmentioning

confidence: 99%

“…We compare with a model that does not account for reciprocity, i.e., our model with η = 0 (DynCRep0) [25].…”

Section: Applicationsmentioning

confidence: 99%

“…Hence, the AUC cannot be calculated for the first time step. In this case we fix K = 3, the minimum number of communities with the highest performance, i.e., we perform 5-fold cross validation [25] to calculate the value of AUC, then we choose K as the number of communities with the highest value for AUC.…”

Section: Statistics Citation Datasetmentioning

confidence: 99%

“…Nevertheless, in directed real-world networks, community membership may not be the only factor influencing network structure. Reciprocity, i.e., the tendency of a pair of nodes to form edges on both directions, has been subject of many studies [23][24][25] as a crucial factor to determine the structure of networks, in particular in social networks. Bartolucci et al [26] assume local conditional independence between pairs of edges, i.e., dyads, and extend the SBM to account for the reciprocal patterns in directed dynamical networks.…”

Section: Introductionmentioning

confidence: 99%

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Reciprocity, community detection, and link prediction in dynamic networks

Safdari¹,

Contisciani²,

Bacco³

2021

Preprint

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Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to model dynamic interactions. Particular interest has been devoted to extend the stochastic block model and its variant, to capture community structure as the network changes in time. While these models assume that edge formation depends only on the community memberships, recent work for static networks show the importance to include additional parameters capturing structural properties, as reciprocity for instance. Remarkably, these models are capable of generating more realistic network representations than those that only consider community membership. To this aim, we present a probabilistic generative model with hidden variables that integrates reciprocity and communities as structural information of networks that evolve in time. The model assumes a fundamental order in observing reciprocal data, that is an edge is observed, conditional on its reciprocated edge in the past. We deploy a Markovian approach to construct the network's transition matrix between time steps and parameters' inference is performed with an Expectation-Maximization algorithm that leads to high computational efficiency because it exploits the sparsity of the dataset. We test the performance of the model on synthetic dynamical networks, as well as on real networks of citations and email datasets. We show that our model captures the reciprocity of real networks better than standard models with only community structure, while performing well at link prediction tasks.

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“…where η as a hyperparameter regulates the reciprocity effects, similarly as in [25]. The difference between Eq.…”

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

“…We compare with a model that does not account for reciprocity, i.e., our model with η = 0 (DynCRep0) [25].…”

Section: Applicationsmentioning

confidence: 99%

Section: Statistics Citation Datasetmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reciprocity, community detection, and link prediction in dynamic networks

Safdari¹,

Contisciani²,

Bacco³

2021

Preprint

Self Cite

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show abstract

Modeling Node Exposure for Community Detection in Networks

Othman

Schulz

Baity‐Jesi

et al. 2023

Complex Networks and Their Applications XI

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Measuring reciprocity: Double sampling, concordance, and network construction

Ready

2021

Net Sci

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Reciprocity—the mutual provisioning of support/goods—is a pervasive feature of social life. Directed networks provide a way to examine the structure of reciprocity in a community. However, measuring social networks involves assumptions about what relationships matter and how to elicit them, which may impact observed reciprocity. In particular, the practice of aggregating multiple sources of data on the same relationship (e.g., “double-sampled” data, where both the “giver” and “receiver” are asked to report on their relationship) may have pronounced impacts on network structure. To investigate these issues, we examine concordance (ties reported by both parties) and reciprocity in a set of directed, double-sampled social support networks. We find low concordance in people’s responses. Taking either the union (including any reported ties) or the intersection (including only concordant ties) of double-sampled relationships results in dramatically higher levels of reciprocity. Using multilevel exponential random graph models of social support networks from 75 villages in India, we show that these changes cannot be fully explained by the increase in the number of ties produced by layer aggregation. Respondents’ tendency to name the same people as both givers and receivers of support plays an important role, but this tendency varies across contexts and relationships type. We argue that no single method should necessarily be seen as the “correct” choice for aggregation of multiple sources of data on a single relationship type. Methods of aggregation should depend on the research question, the context, and the relationship in question.

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Generative model for reciprocity and community detection in networks

Cited by 21 publications

References 46 publications

Reciprocity, community detection, and link prediction in dynamic networks

Reciprocity, community detection, and link prediction in dynamic networks

Modeling Node Exposure for Community Detection in Networks

Measuring reciprocity: Double sampling, concordance, and network construction

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