Consistency landscape of network communities

Lee, Daekyung; Lee, Sang Hoon; Kim, Beom Jun; Kim, Heetae

doi:10.1103/physreve.103.052306

Cited by 10 publications

(22 citation statements)

References 29 publications

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“…Interestingly, the community–node correlation varies with γ , indicating that some communities are more stable than others. This problem exists in most complex networks whenever there are multi-scale interactions governing the organization 36 . Therefore, depending on algorithm design, two community detection methods focusing on slightly different connectivity features may disagree on the optimal node assembly.…”

Section: Discussionmentioning

confidence: 99%

Mapping the semi-nested community structure of 3D chromosome contact networks

Bernenko

Lee

Stenberg

et al. 2022

Preprint

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Mammalian DNA folds into 3D structures that facilitate and regulate genetic processes such as transcription, DNA repair, and epigenetics. Several insights derive from chromosome capture methods, such as Hi-C, which allow researchers to construct contact maps depicting 3D interactions among all DNA segment pairs. These maps show a complex cross-scale organization spanning megabase-pair compartments to short-ranged DNA loops. To better understand the organizing principles, several groups analyzed Hi-C data assuming a Russian-doll-like nested hierarchy where DNA regions of similar sizes merge into larger and larger structures. Apart from being a simple and appealing description, this model explains, e.g., the omnipresent chequerboard pattern seen in Hi-C maps, known as A/B compartments, and foreshadows the co-localization of some functionally similar DNA regions. However, while successful, this model is incompatible with the two competing mechanisms that seem to shape a significant part of the chromosomes' 3D organization: loop extrusion and phase separation. This paper aims to map out the chromosome's actual folding hierarchy from empirical data. To this end, we take advantage of Hi-C experiments and treat the measured DNA-DNA interactions as a weighted network. From such a network, we extract 3D communities using the generalized Louvain algorithm. This algorithm has a resolution parameter that allows us to scan seamlessly through the community size spectrum, from A/B compartments to topologically associated domains (TADs). By constructing a hierarchical tree connecting these communities, we find that chromosomes are more complex than a perfect hierarchy. Analyzing how communities nest relative to a simple folding model, we found that chromosomes exhibit a significant portion of nested and non-nested community pairs alongside considerable randomness. In addition, by examining nesting and chromatin types, we discovered that nested parts are often associated with actively transcribed chromatin. These results highlight that cross-scale relationships will be essential components in models aiming to reach a deep understanding of the causal mechanisms of chromosome folding.

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Section: Discussionmentioning

confidence: 99%

Mapping the semi-nested community structure of 3D chromosome contact networks

Bernenko

Lee

Stenberg

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…To automatically find sub-networks (or communities), we performed community detection using the Leiden algorithm [ 65 ]. In this case, we set the resolution parameter γ = 1.0, which shows consistency in detection [ 66 ]. To calculate modularity and detect modularized communities, we used a Python package, IGRAPH.…”

Section: Methodsmentioning

confidence: 99%

Deciphering clock cell network morphology within the biological master clock, suprachiasmatic nucleus: From the perspective of circadian wave dynamics

et al. 2022

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The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of ~10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (~25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained ‘indegree distribution’ as well as a ‘physical range distribution of afferent clock cells.’ Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced “phase-singularities.” The successful, realistic networks have several common features: 1) “indegree” and “outdegree” should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN.

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“…Random walk is heuristic, so its calculation result is unstable. In addition, some articles focus on the substructure [ 33 ] of networks and analyze the consistency [ 34 , 35 ] and inconsistency [ 36 ] of networks. The main idea of these methods is to analyze the different mesoscopic substructures of the network and distinguish them.…”

Section: Related Workmentioning

confidence: 99%

Joint Detection of Community and Structural Hole Spanner of Networks in Hyperbolic Space

Nie

Jiang

Zhong

et al. 2022

Entropy

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Community detection and structural hole spanner (the node bridging different communities) identification, revealing the mesoscopic and microscopic structural properties of complex networks, have drawn much attention in recent years. As the determinant of mesoscopic structure, communities and structural hole spanners discover the clustering and hierarchy of networks, which has a key impact on transmission phenomena such as epidemic transmission, information diffusion, etc. However, most existing studies address the two tasks independently, which ignores the structural correlation between mesoscale and microscale and suffers from high computational costs. In this article, we propose an algorithm for simultaneously detecting communities and structural hole spanners via hyperbolic embedding (SDHE). Specifically, we first embed networks into a hyperbolic plane, in which, the angular distribution of the nodes reveals community structures of the embedded network. Then, we analyze the critical gap to detect communities and the angular region where structural hole spanners may exist. Finally, we identify structural hole spanners via two-step connectivity. Experimental results on synthetic networks and real networks demonstrate the effectiveness of our proposed algorithm compared with several state-of-the-art methods.

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Consistency landscape of network communities

Cited by 10 publications

References 29 publications

Mapping the semi-nested community structure of 3D chromosome contact networks

Mapping the semi-nested community structure of 3D chromosome contact networks

Deciphering clock cell network morphology within the biological master clock, suprachiasmatic nucleus: From the perspective of circadian wave dynamics

Joint Detection of Community and Structural Hole Spanner of Networks in Hyperbolic Space

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