Post-Processing Partitions to Identify Domains of Modularity Optimization

Gene communities in co-expression networks across different tissues

With the recent availability of tissue-specific gene expression data, e.g., provided by the GTEx Consortium, there is interest in comparing gene co-expression patterns across tissues. One promising approach to this problem is to use a multilayer network analysis framework and perform multilayer community detection. Communities in gene co-expression networks reveal groups of genes similarly expressed across individuals, potentially involved in related biological processes responding to specific environmental stimuli or sharing common regulatory variations. We construct a multilayer network in which each of the four layers is an exocrine gland tissue-specific gene co-expression network. We develop methods for multilayer community detection with correlation matrix input and an appropriate null model. Our correlation matrix input method identifies five groups of genes that are similarly co-expressed in multiple tissues (a community that spans multiple layers, which we call a generalist community) and two groups of genes that are co-expressed in just one tissue (a community that lies primarily within just one layer, which we call a specialist community). We further found gene co-expression communities where the genes physically cluster across the genome significantly more than expected by chance (on chromosomes 1 and 11). This clustering hints at underlying regulatory elements determining similar expression patterns across individuals and cell types. We suggest that KRTAP3-1, KRTAP3-3, and KRTAP3-5 share regulatory elements in skin and pancreas. Furthermore, we find that CELA3A and CELA3B share associated expression quantitative trait loci in the pancreas. The results indicate that our multilayer community detection method for correlation matrix input extracts biologically interesting communities of genes.

The power of weak, transient interactions across biology: A paradigm of emergent behavior

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus.

Gene communities in co-expression networks across different tissues

With the recent availability of tissue-specific gene expression data, e.g., provided by the GTEx Consortium, there is interest in comparing gene co-expression patterns across tissues. One promising approach to this problem is to use a multilayer network analysis framework and perform multilayer community detection. Communities in gene co-expression networks reveal groups of genes similarly expressed across individuals, potentially involved in related biological processes responding to specific environmental stimuli or sharing common regulatory variations. We construct a multilayer network in which each of the four layers is an exocrine gland tissue-specific gene co-expression network. We develop methods for multilayer community detection with correlation matrix input and an appropriate null model. Our correlation matrix input method identifies five groups of genes that are similarly co-expressed in multiple tissues (a community that spans multiple layers, which we call a generalist community) and two groups of genes that are co-expressed in just one tissue (a community that lies primarily within just one layer, which we call a specialist community). We further found gene co-expression communities where the genes physically cluster across the genome significantly more than expected by chance (on chromosomes 1 and 11). This clustering hints at underlying regulatory elements determining similar expression patterns across individuals and cell types. We suggest that KRTAP3-1, KRTAP3-3, and KRTAP3-5 share regulatory elements in skin and pancreas. Furthermore, we find that CELA3A and CELA3B share associated expression quantitative trait loci in the pancreas. The results indicate that our multilayer community detection method for correlation matrix input extracts biologically interesting communities of genes.

Social Media Sentiment about COVID-19 Vaccination Predicts Vaccine Acceptance among Peruvian Social Media Users the Next Day

Drawing upon theories of risk and decision making, we present a theoretical framework for how the emotional attributes of social media content influence risk behaviors. We apply our framework to understanding how COVID-19 vaccination Twitter posts influence acceptance of the vaccine in Peru, the country with the highest relative number of COVID-19 excess deaths. By employing computational methods, topic modeling, and vector autoregressive time series analysis, we show that the prominence of expressed emotions about COVID-19 vaccination in social media content is associated with the daily percentage of Peruvian social media survey respondents who are vaccine-accepting over 231 days. Our findings show that net (positive) sentiment and trust emotions expressed in tweets about COVID-19 are positively associated with vaccine acceptance among survey respondents one day after the post occurs. This study demonstrates that the emotional attributes of social media content, besides veracity or informational attributes, may influence vaccine acceptance for better or worse based on its valence.

A multiresolution framework for the analysis of community structure in international trade networks

International trade networks are complex systems that consist of overlapping multiple trade blocs of varying sizes. However, the resulting structures of community detection in trade networks often fail to accurately represent the complexity of international trade. To address this issue, we propose a multiresolution framework that integrates information from a range of resolutions to consider trade communities of different sizes and reveal the hierarchical structure of trade networks and their constituent blocks. In addition, we introduce a measure called multiresolution membership inconsistency for each country, which demonstrates the positive correlation between a country's structural inconsistency in terms of network topology and its vulnerability to external intervention in terms of economic and security functioning. Our findings show that network science-based approaches can effectively capture the complex interdependencies between countries and provide new metrics for evaluating the characteristics and behaviors of countries in both economic and political contexts.

Finite-state parameter space maps for pruning partitions in modularity-based community detection

Partitioning networks into communities of densely connected nodes is an important tool used widely across different applications, with numerous methods and software packages available for community detection. Modularity-based methods require parameters to be selected (or assume defaults) to control the resolution and, in multilayer networks, interlayer coupling. Meanwhile, most useful algorithms are heuristics yielding different near-optimal results upon repeated runs (even at the same parameters). To address these difficulties, we combine recent developments into a simple-to-use framework for pruning a set of partitions to a subset that are self-consistent by an equivalence with the objective function for inference of a degree-corrected planted partition stochastic block model (SBM). Importantly, this combined framework reduces some of the problems associated with the stochasticity that is inherent in the use of heuristics for optimizing modularity. In our examples, the pruning typically highlights only a small number of partitions that are fixed points of the corresponding map on the set of somewhere-optimal partitions in the parameter space. We also derive resolution parameter upper bounds for fitting a constrained SBM of K blocks and demonstrate that these bounds hold in practice, further guiding parameter space regions to consider. With publicly available code ( http://github.com/ragibson/ModularityPruning ), our pruning procedure provides a new baseline for using modularity-based community detection in practice.

Harmonizing functional connectivity reduces scanner effects in community detection

Community detection on graphs constructed from functional magnetic resonance imaging (fMRI) data has led to important insights into brain functional organization. Large studies of brain community structure often include images acquired on multiple scanners across different studies. Differences in scanner can introduce variability into the downstream results, and these differences are often referred to as scanner effects. Such effects have been previously shown to significantly impact common network metrics. In this study, we identify scanner effects in data-driven community detection results and related network metrics. We assess a commonly employed harmonization method and propose new methodology for harmonizing functional connectivity that leverage existing knowledge about network structure as well as patterns of covariance in the data. Finally, we demonstrate that our new methods reduce scanner effects in community structure and network metrics. Our results highlight scanner effects in studies of brain functional organization and provide additional tools to address these unwanted effects. These findings and methods can be incorporated into future functional connectivity studies, potentially preventing spurious findings and improving reliability of results.

Constant community identification in million-scale networks

The inherently stochastic nature of community detection in real-world complex networks poses an important challenge in assessing the accuracy of the results. In order to eliminate the algorithmic and implementation artifacts, it is necessary to identify the groups of vertices that are always clustered together, independent of the community detection algorithm used. Such groups of vertices are called constant communities. Current approaches for finding constant communities are very expensive and do not scale to large networks. In this paper, we use binary edge classification to find constant communities. The key idea is to classify edges based on whether they form a constant community or not. We present two methods for edge classification. The first is a GCN-based semi-supervised approach that we term Line-GCN. The second is an unsupervised approach based on image thresholding methods. Neither of these methods requires explicit detection of communities and can thus scale to very large networks of the order of millions of vertices. Both of our semi-supervised and unsupervised results on real-world graphs demonstrate that the constant communities obtained by our method have higher F1-scores and comparable or higher NMI scores than other state-of-the-art baseline methods for constant community detection. While the training step of Line-GCN can be expensive, the unsupervised algorithm is 10 times faster than the baseline methods. For larger networks, the baseline methods cannot complete, whereas all of our algorithms can find constant communities in a reasonable amount of time. Finally, we also demonstrate that our methods are robust under noisy conditions. We use three different, well-studied noise models to add noise to the networks and show that our results are mostly stable.

Spectral clustering based on structural magnetic resonance imaging and its relationship with major depressive disorder and cognitive ability

There is increasing interest in using data-driven unsupervised methods to identify structural underpinnings of common mental illnesses, including major depressive disorder (MDD) and associated traits such as cognition. However, studies are often limited to severe clinical cases with small sample sizes and most do not include replication. Here, we examine two relatively large samples with structural magnetic resonance imaging (MRI), measures of lifetime MDD and cognitive variables: Generation Scotland (GS subsample, N = 980) and UK Biobank (UKB, N = 8,900), for discovery and replication, using an exploratory approach. Regional measures of FreeSurfer derived cortical thickness (CT), cortical surface area (CSA), cortical volume (CV) and subcortical volume (subCV) were input into a clustering process, controlling for common covariates. The main analysis steps involved constructing participant K-nearest neighbour graphs and graph partitioning with Markov stability to determine optimal clustering of participants. Resultant clusters were (1) checked whether they were replicated in an independent cohort and (2) tested for associations with depression status and cognitive measures. Participants separated into two clusters based on structural brain measurements in GS subsample, with large Cohen's d effect sizes between clusters in higher order cortical regions, commonly associated with executive function and decision making. Clustering was replicated in the UKB sample, with high correlations of cluster effect sizes for CT, CSA, CV and subCV between cohorts across regions. The identified clusters were not significantly different with respect to MDD case-control status in either cohort (GS subsample: p_FDR  = .2239-.6585; UKB: p_FDR  = .2003-.7690). Significant differences in general cognitive ability were, however, found between the clusters for both datasets, for CSA, CV and subCV (GS subsample: d = 0.2529-.3490, p_FDR  < .005; UKB: d = 0.0868-0.1070, p_FDR  < .005). Our results suggest that there are replicable natural groupings of participants based on cortical and subcortical brain measures, which may be related to differences in cognitive performance, but not to the MDD case-control status.

The modulation of brain network integration and arousal during exploration

There is growing interest in how neuromodulators shape brain networks. Recent neuroimaging studies provide evidence that brainstem arousal systems, such as the locus coeruleus-norepinephrine system (LC-NE), influence functional connectivity and brain network topology, suggesting they have a role in flexibly reconfiguring brain networks in order to adapt behavior and cognition to environmental demands. To date, however, the relationship between brainstem arousal systems and functional connectivity has not been assessed within the context of a task with an established relationship between arousal and behavior, with most prior studies relying on incidental variations in arousal or pharmacological manipulation and static brain networks constructed over long periods of time. These factors have likely contributed to a heterogeneity of effects across studies. To address these issues, we took advantage of the association between LC-NE-linked arousal and exploration to probe the relationships between exploratory choice, arousal—as measured indirectly via pupil diameter—and brain network dynamics. Exploration in a bandit task was associated with a shift toward fewer, more weakly connected modules that were more segregated in terms of connectivity and topology but more integrated with respect to the diversity of cognitive systems represented in each module. Functional connectivity strength decreased, and changes in connectivity were correlated with changes in pupil diameter, in line with the hypothesis that brainstem arousal systems influence the dynamic reorganization of brain networks. More broadly, we argue that carefully aligning dynamic network analyses with task designs can increase the temporal resolution at which behaviorally- and cognitively-relevant modulations can be identified, and offer these results as a proof of concept of this approach.

Consistency landscape of network communities

The concept of community detection has long been used as a key device for handling the mesoscale structures in networks. Suitably conducted community detection reveals various embedded informative substructures of network topology. However, regarding the practical usage of community detection, it has always been a tricky problem to assign a reasonable community resolution for networks of interest. Because of the absence of the unanimously accepted criterion, most of the previous studies utilized rather ad hoc heuristics to decide the community resolution. In this work, we harness the concept of consistency in community structures of networks to provide the overall community resolution landscape of networks, which we eventually take to quantify the reliability of detected communities for a given resolution parameter. More precisely, we exploit the ambiguity in the results of stochastic detection algorithms and suggest a method that denotes the relative validity of community structures in regard to their stability of global and local inconsistency measures using multiple detection processes. Applying our framework to synthetic and real networks, we confirm that it effectively displays insightful fundamental aspects of community structures.

Measurement reliability for individual differences in multilayer network dynamics: Cautions and considerations

Multilayer network models have been proposed as an effective means of capturing the dynamic configuration of distributed neural circuits and quantitatively describing how communities vary over time. Beyond general insights into brain function, a growing number of studies have begun to employ these methods for the study of individual differences. However, test-retest reliabilities for multilayer network measures have yet to be fully quantified or optimized, potentially limiting their utility for individual difference studies. Here, we systematically evaluated the impact of multilayer community detection algorithms, selection of network parameters, scan duration, and task condition on test-retest reliabilities of multilayer network measures (i.e., flexibility, integration, and recruitment). A key finding was that the default method used for community detection by the popular generalized Louvain algorithm can generate erroneous results. Although available, an updated algorithm addressing this issue is yet to be broadly adopted in the neuroimaging literature. Beyond the algorithm, the present work identified parameter selection as a key determinant of test-retest reliability; however, optimization of these parameters and expected reliabilities appeared to be dataset-specific. Once parameters were optimized, consistent with findings from the static functional connectivity literature, scan duration was a much stronger determinant of reliability than scan condition. When the parameters were optimized and scan duration was sufficient, both passive (i.e., resting state, Inscapes, and movie) and active (i.e., flanker) tasks were reliable, although reliability in the movie watching condition was significantly higher than in the other three tasks. The minimal data requirement for achieving reliable measures for the movie watching condition was 20 min, and 30 min for the other three tasks. Our results caution the field against the use of default parameters without optimization based on the specific datasets to be employed - a process likely to be limited for most due to the lack of test-retest samples to enable parameter optimization.

Classification of Long Noncoding RNAs by k-mer Content

K-mer based comparisons have emerged as powerful complements to BLAST-like alignment algorithms, particularly when the sequences being compared lack direct evolutionary relationships. In this chapter, we describe methods to compare k-mer content between groups of long noncoding RNAs (lncRNAs), to identify communities of lncRNAs with related k-mer contents, to identify the enrichment of protein-binding motifs in lncRNAs, and to scan for domains of related k-mer contents in lncRNAs. Our step-by-step instructions are complemented by Python code deposited in Github. Though our chapter focuses on lncRNAs, the methods we describe could be applied to any set of nucleic acid sequences.

Detecting brain network communities: Considering the role of information flow and its different temporal scales

The identification of community structure in graphs continues to attract great interest in several fields. Network neuroscience is particularly concerned with this problem considering the key roles communities play in brain processes and functionality. Most methods used for community detection in brain graphs are based on the maximization of a parameter-dependent modularity function that often obscures the physical meaning and hierarchical organization of the partitions of network nodes. In this work, we present a new method able to detect communities at different scales in a natural, unrestricted way. First, to obtain an estimation of the information flow in the network we release random walkers to freely move over it. The activity of the walkers is separated into oscillatory modes by using empirical mode decomposition. After grouping nodes by their co-occurrence at each time scale, k-modes clustering returns the desired partitions. Our algorithm was first tested on benchmark graphs with favorable performance. Next, it was applied to real and simulated anatomical and/or functional connectomes in the macaque and human brains. We found a clear hierarchical repertoire of community structures in both the anatomical and the functional networks. The observed partitions range from the evident division in two hemispheres -in which all processes are managed globally- to specialized communities seemingly shaped by physical proximity and shared function. Additionally, the spatial scales of a network's community structure (characterized by a measure we term within-communities path length) appear inversely proportional to the oscillatory modes' average frequencies. The proportionality constant may constitute a network-specific propagation velocity for the information flow. Our results stimulate the research of hierarchical community organization in terms of temporal scales of information flow in the brain network.

The community structure of functional brain networks exhibits scale-specific patterns of inter- and intra-subject variability

The network organization of the human brain varies across individuals, changes with development and aging, and differs in disease. Discovering the major dimensions along which this variability is displayed remains a central goal of both neuroscience and clinical medicine. Such efforts can be usefully framed within the context of the brain's modular network organization, which can be assessed quantitatively using computational techniques and extended for the purposes of multi-scale analysis, dimensionality reduction, and biomarker generation. Although the concept of modularity and its utility in describing brain network organization is clear, principled methods for comparing multi-scale communities across individuals and time are surprisingly lacking. Here, we present a method that uses multi-layer networks to simultaneously discover the modular structure of many subjects at once. This method builds upon the well-known multi-layer modularity maximization technique, and provides a viable and principled tool for studying differences in network communities across individuals and within individuals across time. We test this method on two datasets and identify consistent patterns of inter-subject community variability, demonstrating that this variability - which would be undetectable using past approaches - is associated with measures of cognitive performance. In general, the multi-layer, multi-subject framework proposed here represents an advance over current approaches by straighforwardly mapping community assignments across subjects and holds promise for future investigations of inter-subject community variation in clinical populations or as a result of task constraints.

Exploring the solution landscape enables more reliable network community detection

To understand how a complex system is organized and functions, researchers often identify communities in the system's network of interactions. Because it is practically impossible to explore all solutions to guarantee the best one, many community-detection algorithms rely on multiple stochastic searches. But for a given combination of network and stochastic algorithms, how many searches are sufficient to find a solution that is good enough? The standard approach is to pick a reasonably large number of searches and select the network partition with the highest quality or derive a consensus solution based on all network partitions. However, if different partitions have similar qualities such that the solution landscape is degenerate, the single best partition may miss relevant information, and a consensus solution may blur complementary communities. Here we address this degeneracy problem with coarse-grained descriptions of the solution landscape. We cluster network partitions based on their similarity and suggest an approach to determine the minimum number of searches required to describe the solution landscape adequately. To make good use of all partitions, we also propose different ways to explore the solution landscape, including a significance clustering procedure. We test these approaches on synthetic networks and a real-world network using two contrasting community-detection algorithms: The algorithm that can identify more general structures requires more searches, and networks with clearer community structures require fewer searches. We also find that exploring the coarse-grained solution landscape can reveal complementary solutions and enable more reliable community detection.

Comparing Shared Patient Networks Across Payers

BACKGROUND

Measuring care coordination in administrative data facilitates important research to improve care quality.

OBJECTIVE

To compare shared patient networks constructed from administrative claims data across multiple payers.

DESIGN

Social network analysis of pooled cross sections of physicians treating prevalent colorectal cancer patients between 2003 and 2013.

PARTICIPANTS

Surgeons, medical oncologists, and radiation oncologists identified from North Carolina Central Cancer Registry data linked to Medicare claims (N = 1735) and private insurance claims (N = 1321).

MAIN MEASURES

Provider-level measures included the number of patients treated, the number of providers with whom they share patients (by specialty), the extent of patient sharing with each specialty, and network centrality. Network-level measures included the number of providers and shared patients, the density of shared-patient relationships among providers, and the size and composition of clusters of providers with a high level of patient sharing.

RESULTS

For 24.5% of providers, total patient volume rank differed by at least one quintile group between payers. Medicare claims missed 14.6% of all shared patient relationships between providers, but captured a greater number of patient-sharing relationships per provider compared with the private insurance database, even after controlling for the total number of patients (27.242 vs 26.044, p < 0.001). Providers in the private network shared a higher fraction of patients with other providers (0.226 vs 0.127, p < 0.001) compared to the Medicare network. Clustering coefficients for providers, weighted betweenness, and eigenvector centrality varied greatly across payers. Network differences led to some clusters of providers that existed in the combined network not being detected in Medicare alone.

CONCLUSION

Many features of shared patient networks constructed from a single-payer database differed from similar networks constructed from other payers' data. Depending on a study's goals, shortcomings of single-payer networks should be considered when using claims data to draw conclusions about provider behavior.

Transient crosslinking kinetics optimize gene cluster interactions

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5kbp domains (genes) in the nucleolus on Chromosome XII; and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling predictions.

Metabolomic networks connect host-microbiome processes to human Clostridioides difficile infections

Clostridioides difficile infection (CDI) accounts for a substantial proportion of deaths attributable to antibiotic-resistant bacteria in the United States. Although C. difficile can be an asymptomatic colonizer, its pathogenic potential is most commonly manifested in patients with antibiotic-modified intestinal microbiomes. In a cohort of 186 hospitalized patients, we showed that host and microbe-associated shifts in fecal metabolomes had the potential to distinguish patients with CDI from those with non-C. difficile diarrhea and C. difficile colonization. Patients with CDI exhibited a chemical signature of Stickland amino acid fermentation that was distinct from those of uncolonized controls. This signature suggested that C. difficile preferentially catabolizes branched chain amino acids during CDI. Unexpectedly, we also identified a series of noncanonical, unsaturated bile acids that were depleted in patients with CDI. These bile acids may derive from an extended host-microbiome dehydroxylation network in uninfected patients. Bile acid composition and leucine fermentation defined a prototype metabolomic model with potential to distinguish clinical CDI from asymptomatic C. difficile colonization.

Assessing the robustness of cluster solutions obtained from sparse count matrices

Psychological researchers often seek to obtain cluster solutions from sparse count matrices (e.g., social networks; counts of symptoms that are in common for 2 given individuals; structural brain imaging). Increasingly, community detection methods are being used to subset the data in a data-driven manner. While many of these approaches perform well in simulation studies and thus offer some improvement upon traditional clustering approaches, there is no readily available approach for evaluating the robustness of these solutions in empirical data. Researchers have no way of knowing if their results are due to noise. We describe here 2 approaches novel to the field of psychology that enable evaluation of cluster solution robustness. This tutorial also explains the use of an associated R package, perturbR, which provides researchers with the ability to use the methods described herein. In the first approach, the cluster assignment from the original matrix is compared against cluster assignments obtained by randomly perturbing the edges in the matrix. Stable cluster solutions should not demonstrate large changes in the presence of small perturbations. For the second approach, Monte Carlo simulations of random matrices that have the same properties as the original matrix are generated. The distribution of quality scores ("modularity") obtained from the cluster solutions from these matrices are then compared with the score obtained from the original matrix results. From this, one can assess if the results are better than what would be expected by chance. perturbR automates these 2 methods, providing an easy-to-use resource for psychological researchers. We demonstrate the utility of this package using benchmark simulated data generated from a previous study and then apply the methods to publicly available empirical data obtained from social networks and structural neuroimaging. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Functional classification of long non-coding RNAs by k-mer content

The functions of most long non-coding RNAs (lncRNAs) are unknown. In contrast to proteins, lncRNAs with similar functions often lack linear sequence homology; thus, the identification of function in one lncRNA rarely informs the identification of function in others. We developed a sequence comparison method to deconstruct linear sequence relationships in lncRNAs and evaluate similarity based on the abundance of short motifs called kmers. We found that lncRNAs of related function often had similar kmer profiles despite lacking linear homology, and that kmer profiles correlated with protein binding to lncRNAs and with their subcellular localization. Using a novel assay to quantify Xist-like regulatory potential, we directly demonstrated that evolutionarily unrelated lncRNAs can encode similar function through different spatial arrangements of related sequence motifs. Kmer-based classification is a powerful approach to detect recurrent relationships between sequence and function in lncRNAs.

Multiresolution Consensus Clustering in Networks

Networks often exhibit structure at disparate scales. We propose a method for identifying community structure at different scales based on multiresolution modularity and consensus clustering. Our contribution consists of two parts. First, we propose a strategy for sampling the entire range of possible resolutions for the multiresolution modularity quality function. Our approach is directly based on the properties of modularity and, in particular, provides a natural way of avoiding the need to increase the resolution parameter by several orders of magnitude to break a few remaining small communities, necessitating the introduction of ad-hoc limits to the resolution range with standard sampling approaches. Second, we propose a hierarchical consensus clustering procedure, based on a modified modularity, that allows one to construct a hierarchical consensus structure given a set of input partitions. While here we are interested in its application to partitions sampled using multiresolution modularity, this consensus clustering procedure can be applied to the output of any clustering algorithm. As such, we see many potential applications of the individual parts of our multiresolution consensus clustering procedure in addition to using the procedure itself to identify hierarchical structure in networks.