Multiscale community detection in Cytoscape.

Detection of community structure has become a fundamental step in the analysis of biological networks with application to protein function annotation, disease gene prediction, and drug discovery. This recent impact creates a need to make these techniques and their accompanying visualization schemes available to a broad range of biologists. Here we present a service-oriented, end-to-end software framework, CDAPS (Community Detection APplication and Service), that integrates the identification, annotation, visualization, and interrogation of multiscale network communities, accessible within the popular Cytoscape network analysis platform. With novel design principles, CDAPS addresses unmet new challenges, such as identifying hierarchical community structures, comparison of outputs generated from diverse network resources, and easy deployment of new algorithms, to facilitate community-sourced science. We demonstrate that the CDAPS framework can be applied to high-throughput protein-protein interaction networks to gain novel insights, such as the identification of putative new members of known protein complexes.

Subsystem organization of axonal connections within and between the right and left cerebral cortex and cerebral nuclei (endbrain).

The endbrain (telencephalon) is at the rostral end of the central nervous system and is primarily responsible for supporting cognition and affect. Structurally, it consists of right and left cerebral hemispheres, each parceled into multiple cortical and nuclear gray matter regions. The global network organization of axonal macroconnections between the 244 regions forming the endbrain was analyzed with a multiresolution consensus clustering (MRCC) method that provides a hierarchical description of community clustering (modules or subsystems) within the network. Experimental evidence was collated from the neuroanatomical literature for the existence of 10,002 of a possible 59,292 connections within the network, and they cluster into four top-level subsystems and 60 bottom-level subsystems arranged in a 50-level hierarchy. Two top-level subsystems are bihemispheric: One deals with auditory and visual information, and the other corresponds broadly to the default mode network. The other two top-level subsystems are bilaterally symmetrical, and each deals broadly with somatic and visceral information. Because the entire endbrain connection matrix was assembled from multiple subconnectomes, it was easy to show that the status of a region as a connectivity hub is not absolute but, instead, depends on the size and coverage of its anatomical neighborhood. It was also shown numerically that creating an ultradense connection matrix by converting all "absent" connections to a "very weak" connection weight has virtually no effect on the clustering hierarchy. The next logical step in this project is to complete the forebrain connectome by adding the thalamus and hypothalamus (together, the interbrain) to the endbrain analysis.

Reconfiguration of Cortical Networks in MDD Uncovered by Multiscale Community Detection with fMRI.

Major depressive disorder (MDD) is known to be associated with altered interactions between distributed brain regions. How these regional changes relate to the reorganization of cortical functional systems, and their modulation by antidepressant medication, is relatively unexplored. To identify changes in the community structure of cortical functional networks in MDD, we performed a multiscale community detection algorithm on resting-state functional connectivity networks of unmedicated MDD (uMDD) patients (n = 46), medicated MDD (mMDD) patients (n = 38), and healthy controls (n = 50), which yielded a spectrum of multiscale community partitions. we selected an optimal resolution level by identifying the most stable community partition for each group. uMDD and mMDD groups exhibited a similar reconfiguration of the community structure of the visual association and the default mode systems but showed different reconfiguration profiles in the frontoparietal control (FPC) subsystems. Furthermore, the central system (somatomotor/salience) and 3 frontoparietal subsystems showed strengthened connectivity with other communities in uMDD but, with the exception of 1 frontoparietal subsystem, returned to control levels in mMDD. These findings provide evidence for reconfiguration of specific cortical functional systems associated with MDD, as well as potential effects of medication in restoring disease-related network alterations, especially those of the FPC system.

Reputation and impact in academic careers.

Reputation is an important social construct in science, which enables informed quality assessments of both publications and careers of scientists in the absence of complete systemic information. However, the relation between reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods. Here, we develop an original framework for measuring how a publication's citation rate Δc depends on the reputation of its central author i, in addition to its net citation count c. To estimate the strength of the reputation effect, we perform a longitudinal analysis on the careers of 450 highly cited scientists, using the total citations Ci of each scientist as his/her reputation measure. We find a citation crossover c×, which distinguishes the strength of the reputation effect. For publications with c < c×, the author's reputation is found to dominate the annual citation rate. Hence, a new publication may gain a significant early advantage corresponding to roughly a 66% increase in the citation rate for each tenfold increase in Ci. However, the reputation effect becomes negligible for highly cited publications meaning that, for c ≥ c×, the citation rate measures scientific impact more transparently. In addition, we have developed a stochastic reputation model, which is found to reproduce numerous statistical observations for real careers, thus providing insight into the microscopic mechanisms underlying cumulative advantage in science.

Adding network structure onto the map of collective behavior.

We propose an extension to the map of Bentley et al. by incorporating an aspect of underlying network structure that is likely relevant for many modes of collective behavior. This dimension, which captures a feature of network community structure, is known both from theory and from experiments to be relevant for decision-making processes.

Symmetry breaking in optimal transport networks.

Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite limited. Not much is known about how the topology of the optimal network changes as a function of its size, the relative efficiency of its layers, and the cost of switching between layers. Here, we show that optimal networks undergo sharp transitions from symmetric to asymmetric shapes, indicating that it is sometimes better to avoid serving a whole area to save on switching costs. Also, we analyze the real transportation networks of the cities of Atlanta, Boston, and Toronto using our theoretical framework and find that they are farther away from their optimal shapes as traffic congestion increases.

Collaboration and topic switches in science.

Collaboration is a key driver of science and innovation. Mainly motivated by the need to leverage different capacities and expertise to solve a scientific problem, collaboration is also an excellent source of information about the future behavior of scholars. In particular, it allows us to infer the likelihood that scientists choose future research directions via the intertwined mechanisms of selection and social influence. Here we thoroughly investigate the interplay between collaboration and topic switches. We find that the probability for a scholar to start working on a new topic increases with the number of previous collaborators, with a pattern showing that the effects of individual collaborators are not independent. The higher the productivity and the impact of authors, the more likely their coworkers will start working on new topics. The average number of coauthors per paper is also inversely related to the topic switch probability, suggesting a dilution of this effect as the number of collaborators increases.

Influence maximization: Divide and conquer.

The problem of influence maximization, i.e., finding the set of nodes having maximal influence on a network, is of great importance for several applications. In the past two decades, many heuristic metrics to spot influencers have been proposed. Here, we introduce a framework to boost the performance of such metrics. The framework consists in dividing the network into sectors of influence, and then selecting the most influential nodes within these sectors. We explore three different methodologies to find sectors in a network: graph partitioning, graph hyperbolic embedding, and community structure. The framework is validated with a systematic analysis of real and synthetic networks. We show that the gain in performance generated by dividing a network into sectors before selecting the influential spreaders increases as the modularity and heterogeneity of the network increase. Also, we show that the division of the network into sectors can be efficiently performed in a time that scales linearly with the network size, thus making the framework applicable to large-scale influence maximization problems.

Robustness modularity in complex networks.

A basic question in network community detection is how modular a given network is. This is usually addressed by evaluating the quality of partitions detected in the network. The Girvan-Newman (GN) modularity function is the standard way to make this assessment, but it has a number of drawbacks. Most importantly, it is not clearly interpretable, given that the measure can take relatively large values on partitions of random networks without communities. Here we propose a measure based on the concept of robustness: modularity is the probability to find trivial partitions when the structure of the network is randomly perturbed. This concept can be implemented for any clustering algorithm capable of telling when a group structure is absent. Tests on artificial and real graphs reveal that robustness modularity can be used to assess and compare the strength of the community structure of different networks. We also introduce two other quality functions: modularity difference, a suitably normalized version of the GN modularity, and information modularity, a measure of distance based on information compression. Both measures are strongly correlated with robustness modularity, but have lower time complexity, so they could be used on networks whose size makes the calculation of robustness modularity too costly.

Universality of citation distributions: toward an objective measure of scientific impact.

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited c times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator c(f) = c/c(0) is considered, where c(0) is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of c(f) as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h index suitable for comparing scientists working in different fields.

Community detection in networks using graph embeddings.

Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the identification of network communities as well because nodes in the same community should be projected close to each other in the geometric space, where they can be detected via standard data clustering algorithms. In this paper, we test the ability of several graph embedding techniques to detect communities on benchmark graphs. We compare their performance against that of traditional community detection algorithms. We find that the performance is comparable, if the parameters of the embedding techniques are suitably chosen. However, the optimal parameter set varies with the specific features of the benchmark graphs, like their size, whereas popular community detection algorithms do not require any parameter. So, it is not possible to indicate beforehand good parameter sets for the analysis of real networks. This finding, along with the high computational cost of embedding a network and grouping the points, suggests that, for community detection, current embedding techniques do not represent an improvement over network clustering algorithms.

Characterizing and modeling the dynamics of online popularity.

Online popularity has an enormous impact on opinions, culture, policy, and profits. We provide a quantitative, large scale, temporal analysis of the dynamics of online content popularity in two massive model systems: the Wikipedia and an entire country's Web space. We find that the dynamics of popularity are characterized by bursts, displaying characteristic features of critical systems such as fat-tailed distributions of magnitude and interevent time. We propose a minimal model combining the classic preferential popularity increase mechanism with the occurrence of random popularity shifts due to exogenous factors. The model recovers the critical features observed in the empirical analysis of the systems analyzed here, highlighting the key factors needed in the description of popularity dynamics.

Scientific elite revisited: patterns of productivity, collaboration, authorship and impact.

Throughout history, a relatively small number of individuals have made a profound and lasting impact on science and society. Despite long-standing, multi-disciplinary interests in understanding careers of elite scientists, there have been limited attempts for a quantitative, career-level analysis. Here, we leverage a comprehensive dataset we assembled, allowing us to trace the entire career histories of nearly all Nobel laureates in physics, chemistry, and physiology or medicine over the past century. We find that, although Nobel laureates were energetic producers from the outset, producing works that garner unusually high impact, their careers before winning the prize follow relatively similar patterns to those of ordinary scientists, being characterized by hot streaks and increasing reliance on collaborations. We also uncovered notable variations along their careers, often associated with the Nobel Prize, including shifting coauthorship structure in the prize-winning work, and a significant but temporary dip in the impact of work they produce after winning the Nobel Prize. Together, these results document quantitative patterns governing the careers of scientific elites, offering an empirical basis for a deeper understanding of the hallmarks of exceptional careers in science.

Explosive percolation in scale-free networks.

We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a nonvanishing percolation threshold already for lambda>lambda(c) approximately 2.2. More interestingly, the transition is continuous when lambda3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.

Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities.

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogeneous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, such as social networks. As a practical application, we show how modularity optimization performs on our benchmark.

Renormalization flows in complex networks.

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social, and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

A dataset of publication records for Nobel laureates.

A central question in the science of science concerns how to develop a quantitative understanding of the evolution and impact of individual careers. Over the course of history, a relatively small fraction of individuals have made disproportionate, profound, and lasting impacts on science and society. Despite a long-standing interest in the careers of scientific elites across diverse disciplines, it remains difficult to collect large-scale career histories that could serve as training sets for systematic empirical and theoretical studies. Here, by combining unstructured data collected from CVs, university websites, and Wikipedia, together with the publication and citation database from Microsoft Academic Graph (MAG), we reconstructed publication histories of nearly all Nobel prize winners from the past century, through both manual curation and algorithmic disambiguation procedures. Data validation shows that the collected dataset presents among the most comprehensive collection of publication records for Nobel laureates currently available. As our quantitative understanding of science deepens, this dataset is expected to have increasing value. It will not only allow us to quantitatively probe novel patterns of productivity, collaboration, and impact governing successful scientific careers, it may also help us unearth the fundamental principles underlying creativity and the genesis of scientific breakthroughs.

Fast consensus clustering in complex networks.

Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions than the ones obtained by the direct application of the algorithm. However, the procedure requires the calculation of the consensus matrix, which can be quite dense if (some of) the clusters of the input partitions are large. Consequently, the complexity can get dangerously close to quadratic, which makes the technique inapplicable on large graphs. Here, we present a fast variant of consensus clustering, which calculates the consensus matrix only on the links of the original graph and on a comparable number of additional node pairs, suitably chosen. This brings the complexity down to linear, while the performance remains comparable as the full technique. Therefore, our fast consensus clustering procedure can be applied on networks with millions of nodes and links.

Resting state network modularity along the prodromal late onset Alzheimer's disease continuum.

Alzheimer's disease is considered a disconnection syndrome, motivating the use of brain network measures to detect changes in whole-brain resting state functional connectivity (FC). We investigated changes in FC within and among resting state networks (RSN) across four different stages in the Alzheimer's disease continuum. FC changes were examined in two independent cohorts of individuals (84 and 58 individuals, respectively) each comprising control, subjective cognitive decline, mild cognitive impairment and Alzheimer's dementia groups. For each participant, FC was computed as a matrix of Pearson correlations between pairs of time series from 278 gray matter brain regions. We determined significant differences in FC modular organization with two distinct approaches, network contingency analysis and multiresolution consensus clustering. Network contingency analysis identified RSN sub-blocks that differed significantly across clinical groups. Multiresolution consensus clustering identified differences in the stability of modules across multiple spatial scales. Significant modules were further tested for statistical association with memory and executive function cognitive domain scores. Across both analytic approaches and in both participant cohorts, the findings converged on a pattern of FC that varied systematically with diagnosis within the frontoparietal network (FP) and between the FP network and default mode network (DMN). Disturbances of modular organization were manifest as greater internal coherence of the FP network and stronger coupling between FP and DMN, resulting in less segregation of these two networks. Our findings suggest that the pattern of interactions within and between specific RSNs offers new insight into the functional disruption that occurs across the Alzheimer's disease spectrum.