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A quantitative understanding of people’s mobility patterns is crucial for many applications. However, it is difficult to accurately estimate mobility, in particular during disruption such as the onset of the COVID-19 pandemic. Here, we investigate the use of multiple sources of data from mobile phones, road traffic sensors, and companies such as Google and Facebook in modelling mobility patterns, with the aim of estimating mobility flows in Finland in early 2020, before and during the disruption induced by the pandemic. We find that the highest accuracy is provided by a model that combines a past baseline from mobile phone data with up-to-date road traffic data, followed by the radiation and gravity models similarly augmented with traffic data. Our results highlight the usefulness of publicly available road traffic data in mobility modelling and, in general, pave the way for a data fusion approach to estimating mobility flows.

The Lawrence Berkeley National Laboratory working group was presented with three problems involving the improvement of images from an AFM scanner. The first concerned the inpainting of an image for which data is collected via a spiral scan waveform. The second concerned the exploitation of data obtained at different times to obtain better spatial resolution. The third concerned the correction of horizontal positions reported by the sensor, particularly when the scanner is operating at high frequency. Herein is a brief report on the progress and ideas generated by the working group on each of these problems.

We study how the herd immunity threshold and the expected epidemic size depend on homophily with respect to vaccine adoption. We find that the presence of homophily considerably increases the critical vaccine coverage needed for herd immunity and that strong homophily can push the threshold entirely out of reach. The epidemic size monotonically increases as a function of homophily strength for a perfect vaccine, while it is maximized at a nontrivial level of homophily when the vaccine efficacy is limited. Our results highlight the importance of vaccination homophily in epidemic modeling., 12 pages, 9 figures

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similarly to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and, otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low-dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks.

Contact tracing via digital tracking applications installed on mobile phones is an important tool for controlling epidemic spreading. Its effectivity can be quantified by modifying the standard methodology for analyzing percolation and connectivity of contact networks. We apply this framework to networks with varying degree distributions, numbers of application users, and probabilities of quarantine failures. Further, we study structured populations with homophily and heterophily and the possibility of degree-targeted application distribution. Our results are based on a combination of explicit simulations and mean-field analysis. They indicate that there can be major differences in the epidemic size and epidemic probabilities which are equivalent in the normal susceptible-infectious-recovered (SIR) processes. Further, degree heterogeneity is seen to be especially important for the epidemic threshold but not as much for the epidemic size. The probability that tracing leads to quarantines is not as important as the application adoption rate. Finally, both strong homophily and especially heterophily with regard to application adoption can be detrimental. Overall, epidemic dynamics are very sensitive to all of the parameter values we tested out, which makes the problem of estimating the effect of digital contact tracing an inherently multidimensional problem.

We evaluate the efficiency of various heuristic strategies for allocating vaccines against COVID-19 and compare them to strategies found using optimal control theory. Our approach is based on a mathematical model which tracks the spread of disease among different age groups and across different geographical regions, and we introduce a method to combine age-specific contact data to geographical movement data. As a case study, we model the epidemic in the population of mainland Finland utilizing mobility data from a major telecom operator. Our approach allows to determine which geographical regions and age groups should be targeted first in order to minimize the number of deaths. In the scenarios that we test, we find that distributing vaccines demographically and in an age-descending order is not optimal for minimizing deaths and the burden of disease. Instead, more lives could be saved by using strategies which emphasize high-incidence regions and distribute vaccines in parallel to multiple age groups. The level of emphasis that high-incidence regions should be given depends on the overall transmission rate in the population. This observation highlights the importance of updating the vaccination strategy when the effective reproduction number changes due to the general contact patterns changing and new virus variants entering.

Characterising the spreading of ideas within echo chambers is essential for understanding polarisation. In this article, we explore the characteristics of popular and viral content in climate change discussions on Twitter around the 2019 announcement of the Nobel Peace Prize, where we find the retweet network of users to be polarised into two well-separated groups of activists and sceptics. Operationalising popularity as the number of retweets and virality as the spreading probability inferred using an independent cascade model, we find that the viral themes echo and differ from the popular themes in interesting ways. Most importantly, we find that the most viral themes in the two groups reflect different types of bonds that tie the community together, yet both function to enhance ingroup connections while repulsing outgroup engagement. With this, our study sheds light, from an information-spreading perspective, on the formation and upkeep of echo chambers in climate discussions.

Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for multilayer networks which allows one to break any multilayer network into small multilayered building blocks. These multilayer graphlets can be either analyzed themselves or used to do tasks such as comparing different systems. The method is flexible in terms of multilayer isomorphism, automorphism orbit definition, and the type of multilayer network. We illustrate our method for multiplex networks and show how it can be used to distinguish networks produced with multiple models from each other in an unsupervised way. In addition, we include an automatic way of generating the hundreds of dependency equations between the orbit counts needed to remove redundant orbit counts. The framework introduced here allows one to analyze multilayer networks with versatile semantics, and these methods can thus be used to analyze the structural building blocks of myriad multilayer networks., Comment: 58 pages, 45 figures

In all of science, the authors of publications depend on the knowledge presented by the previous publications. Thus they "stand on the shoulders of giants" and there is a flow of knowledge from previous publications to more recent ones. The dominating paradigm for tracking this flow of knowledge is to count the number of direct citations, but this neglects the fact that beneath the first layer of citations there is a full body of literature. In this study, we go underneath the "shoulders" by investigating the cumulative knowledge creation process in a citation network of around 35 million publications. In particular, we study stylized models of persistent influence and diffusion that take into account all the possible chains of citations. When we study the persistent influence values of publications and their citation counts, we find that the publications related to Nobel prizes, i.e., Nobel papers have higher ranks in terms of persistent influence than that due to citations, and that the most outperforming publications are typically early works leading to hot research topics of their time. The diffusion model reveals a significant variation in the rates at which different fields of research share knowledge. We find that these rates have been increasing systematically for several decades, which can be explained by the increase in the publication volumes. Overall, our results suggest that analyzing cumulative knowledge creation on a global scale can be useful in estimating the type and scale of scientific influence of individual publications and entire research areas as well as yielding insights that could not be discovered by using only the direct citation counts.

Investors in stock markets face a huge amount of financial information. For that reason, they must decide how to distribute their limited attention across different securities. We propose a new measure of investor attention, called the trading signature. This measure allows us to analyze whether there are heterogeneous, persistent, and characteristic patterns in the way how investors distribute their attention. Our study builds on a large data set that contains every transaction of hundreds of thousands of households and financial institutions in a stock market for over 20 years. We find that the ways how investors distribute their attention are not only distinctive but invariant with respect to changes in their portfolios. Moreover, investor behavior is surprisingly persistent: it takes at least seven years for an investor to significantly change her attention distribution. These observations are strikingly similar to recent findings on how people manage their social networks. However, in contrast to social relationships, time constraints do not appear to limit investors’ activeness in the markets: the larger is an investor’s portfolio, the more frequently each security is traded on average. A possible explanation is that different trading strategies require different amounts of effort, and an investor can switch between the strategies if she changes the size of her portfolio.

Prior research shows that public opinion on climate politics sorts along partisan lines. However, they leave open the question of whether climate politics and other politically salient issues exhibit tendencies for issue alignment, which the political polarization literature identifies as among the most deleterious aspects of polarization. Using a network approach and social media data from the Twitter platform, we study polarization of public opinion toward climate politics and ten other politically salient topics during the 2019 Finnish elections as the emergence of opposing groups in a public forum. We find that while climate politics is not particularly polarized compared to the other topics, it is subject to partisan sorting and issue alignment within the universalist-communitarian dimension of European politics that arose following the growth of right-wing populism. Notably, climate politics is consistently aligned with the immigration issue, and temporal trends indicate that this phenomenon will likely persist., Comment: Working paper, 30 pages, 6 figures

Time-limited states characterize many dynamical processes on networks: disease-infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These dynamics can be described as limited-waiting-time processes, and they are particularly important for systems modeled as temporal networks. These processes have been studied via simulations, which is equivalent to repeatedly finding all limited-waiting-time temporal paths from a source node and time. We propose a method yielding an orders-of-magnitude more efficient way of tracking the reachability of such temporal paths. Our method gives simultaneous estimates of the in- or out-reachability (with any chosen waiting-time limit) from every possible starting point and time. It works on very large temporal networks with hundreds of millions of events on current commodity computing hardware. This opens up the possibility to analyze reachability and dynamics of spreading processes on large temporal networks in completely new ways. For example, one can now compute centralities based on global reachability for all events or can find with high probability the infected node and time, which would lead to the largest epidemic outbreak.

Comprehensive characterization of non-Poissonian, bursty temporal patterns observed in various natural and social processes is crucial to understand the underlying mechanisms behind such temporal patterns. Among them bursty event sequences have been studied mostly in terms of interevent times (IETs), while the higher-order correlation structure between IETs has gained very little attention due to the lack of a proper characterization method. In this paper we propose a method of decomposing an event sequence into a set of IETs and a burst tree, which exactly captures the structure of temporal correlations that is entirely missing in the analysis of IET distributions. We apply the burst-tree decomposition method to various datasets and analyze the structure of the revealed burst trees. In particular, we observe that event sequences show similar burst-tree structure, such as heavy-tailed burst size distributions, despite of very different IET distributions. The burst trees allow us to directly characterize the preferential and assortative mixing structure of bursts responsible for the higher-order temporal correlations. We also show how to use the decomposition method for the systematic investigation of such higher-order correlations captured by the burst trees in the framework of randomized reference models. Finally, we devise a simple kernel-based model for generating event sequences showing appropriate higher-order temporal correlations. Our method is a tool to make the otherwise overwhelming analysis of higher-order correlations in bursty time series tractable by turning it into the analysis of a tree structure., 10 pages, 4 figures

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may, for example, be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use nontrivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs) that sample networks with uniform probability. Focusing on temporal networks, we survey applications of MRRMs found in the literature, and we use this framework to build a taxonomy of MRRMs that proposes a canonical naming convention, classifies them, and deduces their effects on a range of important network features. We furthermore show that certain classes of MRRMs may be applied in sequential composition to generate new MRRMs from the existing ones surveyed in this article. We finally provide a tutorial showing how to apply a series of MRRMs to analyze how different network features affect a dynamic process in an empirical temporal network., Comment: Accepted version

International audience; The notion of multi-layer networks introduces a general framework and common vocabulary for existing ideas in complex network theory. In doing so, it is possible to understand and compare these dierent ideas in a new and more fruitful manner. However, to make this operationalizable to the visualization and visual analytics community, we need more clarity. For example: What is a layer? What are the semantics of interlayer edges, and specifically, identity links between layers? Can dierent multilayered networks be expressed or implemented in the same way? And vice versa, can one multilayered network be expressed or implemented in dierent ways?

The times of temporal-network events and their correlations contain information on the function of the network and they influence dynamical processes taking place on it. To extract information out of correlated event times, techniques such as the analysis of temporal motifs have been developed. In this Chapter, we discuss a recently-introduced, more general framework that maps temporal-network structure into static graphs while retaining information on time-respecting paths and the time differences between their consequent events. This framework builds on weighted temporal event graphs: directed, acyclic graphs (DAGs) that contain a superposition of all temporal paths. We introduce the reader to the temporal event-graph mapping and associated computational methods and illustrate its use by applying the framework to temporal-network percolation.

We identify temporal investor networks for Nokia stock by constructing networks from correlations between investor-specific net-volumes and analyze changes in the networks around dot-com bubble. We conduct the analysis separately for households, non-financial institutions, and financial institutions. Our results indicate that spanning tree measures for households reflected the boom and crisis: the maximum spanning tree measures had clear upward tendency in the bull markets when the bubble was building up, and, even more importantly, the minimum spanning tree measures pre-reacted the burst of bubble. At the same time, we find less clear reactions in minimal and maximal spanning trees of non-financial and financial institutions around the bubble, which suggest that household investors can have a greater herding tendency around bubbles., 15 pages, 4 figures

This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new links is dependent on the (typically local) network structure (network evolution models, NEMs), and those in which links are generated based only on nodal attributes (nodal attribute models, NAMs). An exponential random graph model (ERGM) with structural dependencies is included for comparison. We fit models from each of these categories to two empirical acquaintance networks with respect to basic network properties. We compare higher order structures in the resulting networks with those in the data, with the aim of determining which models produce the most realistic network structure with respect to degree distributions, assortativity, clustering spectra, geodesic path distributions, and community structure (subgroups with dense internal connections). We find that the nodal attribute models successfully produce assortative networks and very clear community structure. However, they generate unrealistic clustering spectra and peaked degree distributions that do not match empirical data on large social networks. On the other hand, many of the network evolution models produce degree distributions and clustering spectra that agree more closely with data. They also generate assortative networks and community structure, although often not to the same extent as in the data. The ERGM model, which turned out to be near-degenerate in the parameter region best fitting our data, produces the weakest community structure.

A diverse variety of processes --- including recurrent disease episodes, neuron firing, and communication patterns among humans --- can be described using inter-event time (IET) distributions. Many such processes are ongoing, although event sequences are only available during a finite observation window. Because the observation time window is more likely to begin or end during long IETs than during short ones, the analysis of such data is susceptible to a bias induced by the finite observation period. In this paper, we illustrate how this length bias is born and how it can be corrected without assuming any particular shape for the IET distribution. To do this, we model event sequences using stationary renewal processes, and we formulate simple heuristics for determining the severity of the bias. To illustrate our results, we focus on the example of empirical communication networks, which are temporal networks that are constructed from communication events. The IET distributions of such systems guide efforts to build models of human behavior, and the variance of IETs is very important for estimating the spreading rate of information in networks of temporal interactions. We analyze several well-known data sets from the literature, and we find that the resulting bias can lead to systematic underestimates of the variance in the IET distributions and that correcting for the bias can lead to qualitatively different results for the tails of the IET distributions., 11 pages, 7 figures; Software used for the analysis: http://github.com/bolozna/iet

We extend the concept of graph isomorphisms to multilayer networks with any number of "aspects" (i.e., types of layering). In developing this generalization, we identify multiple types of isomorphisms. For example, in multilayer networks with a single aspect, permuting vertex labels, layer labels, and both vertex labels and layer labels each yield different isomorphism relations between multilayer networks. Multilayer network isomorphisms lead naturally to defining isomorphisms in any of the numerous types of networks that can be represented as a multilayer network, and we thereby obtain isomorphisms for multiplex networks, temporal networks, networks with both of these features, and more. We reduce each of the multilayer network isomorphism problems to a graph isomorphism problem, where the size of the graph isomorphism problem grows linearly with the size of the multilayer network isomorphism problem. One can thus use software that has been developed to solve graph isomorphism problems as a practical means for solving multilayer network isomorphism problems. Our theory lays a foundation for extending many network analysis methods --- including motifs, graphlets, structural roles, and network alignment --- to any multilayer network., Comment: Working paper; 18 pages, 7 figures

International audience; The recent application of graph-based network theory analysis to biogeography, community ecology and population genetics has created a need for user-friendly software, which would allow a wider accessibility to and adaptation of these methods. EDENetworks aims to fill this void by providing an easy-to-use interface for the whole analysis pipeline of ecological and evolutionary networks starting from matrices of species distributions, genotypes, bacterial OTUs or populations characterized genetically. The user can choose between several different ecological distance metrics, such as Bray-Curtis or Sorensen distance, or population genetic metrics such as FST or Goldstein distances, to turn the raw data into a distance/dissimilarity matrix. This matrix is then transformed into a network by manual or automatic thresholding based on percolation theory or by building the minimum spanning tree. The networks can be visualized along with auxiliary data and analysed with various metrics such as degree, clustering coefficient, assortativity and betweenness centrality. The statistical significance of the results can be estimated either by resampling the original biological data or by null models based on permutations of the data.

Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different "layers" that each represent one of many possible subsystems or types of interactions. Nevertheless, it is traditional to aggregate multilayer networks into a single weighted network in order to take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic, as important information can be lost as a result. It is therefore important to develop multilayer generalizations of network concepts. In this paper, we analyze triadic relations and generalize the idea of transitivity to multiplex networks. By focusing on triadic relations, which yield the simplest type of transitivity, we generalize the concept and computation of clustering coefficients to multiplex networks. We show how the layered structure of such networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute multiplex clustering coefficients for several real multiplex networks and illustrate why one must take great care when generalizing standard network concepts to multiplex networks. We also derive analytical expressions for our clustering coefficients for ensemble averages of networks in a family of random multiplex networks. Our analysis illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. These insights are invisible if one only studies aggregated networks., Main text + Supplementary Material included in a single file. Published in New Journal of Physics

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook., Working paper; 59 pages, 8 figures

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is very rich. Achieving a deep understanding of such systems necessitates generalizing "traditional" network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multi-layer complex systems. In this paper, we introduce a tensorial framework to study multi-layer networks, and we discuss the generalization of several important network descriptors and dynamical processes --including degree centrality, clustering coefficients, eigenvector centrality, modularity, Von Neumann entropy, and diffusion-- for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multi-layer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems., 15 pages, 5 figures

The aim of this work was to study the similarity network and hierarchical clustering of Finnish emotion concepts. Native speakers of Finnish evaluated similarity between the 50 most frequently used Finnish words describing emotional experiences. We hypothesized that methods developed within network theory, such as identifying clusters and specific local network structures, can reveal structures that would be difficult to discover using traditional methods such as multidimensional scaling (MDS) and ordinary cluster analysis. The concepts divided into three main clusters, which can be described as negative, positive, and surprise. Negative and positive clusters divided further into meaningful sub-clusters, corresponding to those found in previous studies. Importantly, this method allowed the same concept to be a member in more than one cluster. Our results suggest that studying particular network structures that do not fit into a low-dimensional description can shed additional light on why subjects evaluate certain concepts as similar. To encourage the use of network methods in analyzing similarity data, we provide the analysis software for free use (http://www.becs.tkk.fi/similaritynets/).

In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how a dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and a susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network. With the help of temporal networks derived from large-scale time-stamped data on mobile phone calls, we extend earlier results that indicate the slowing-down effects of burstiness and temporal inhomogeneities. In such networks, links are not permanently active, but dynamic processes are mediated by recurrent events taking place on the links at specific points in time. We perform a multiscale analysis and pinpoint the importance of the timings of event sequences on individual links, their correlations with neighboring sequences, and the temporal pathways taken by the network-scale spreading process. This is achieved by studying empirically and analytically different characteristic relay times of links, relevant to the respective scales, and a set of temporal reference models that allow for removing selected time-domain correlations one by one. Our analysis shows that for the spreading velocity, time-domain inhomogeneities are as important as the network topology, which indicates the need to take time-domain information into account when studying spreading dynamics. In particular, results for the different characteristic relay times underline the importance of the burstiness of individual links.

We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural properties of the network as well as the number of unoccupied links considered for comparison in our procedure. We observe that in our social networks, the percolation clusters close to the critical point are related to the community structure. This relationship is further highlighted by applying the procedure to model networks with pre-defined communities., 6 pages, 4 figures. Published version. Elongated to include the results and figures of finite-size scaling and modularity analysis

While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible-infected model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks. We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as ``fingerprints'' of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category. Our findings are verified by the use of two fundamentally different community detection methods., Comment: 15 pages, 20 figures, 4 tables