We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

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Finding and evaluating community structure in networks.

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as ``modularity'' over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.

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Finding community structure in networks using the eigenvectors of matrices

Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labeled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.

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Link prediction in complex networks: A survey

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems In many cases, however, the edges are not continuously active As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts In some cases, edges are active for non-negligible periods of time: eg, the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Temporal Networks

There has been considerable recent interest in algorithms for finding communities in networks— groups of vertices within which connections are dense, but between which connections are sparser. Here we review the progress that has been made towards this end. We begin by describing some traditional methods of community detection, such as spectral bisection, the Kernighan-Lin algorithm and hierarchical clustering based on similarity measures. None of these methods, however, is ideal for the types of real-world network data with which current research is concerned, such as Internet and web data and biological and social networks. We describe a number of more recent algorithms that appear to work well with these data, including algorithms based on edge betweenness scores, on counts of short loops in networks and on voltage differences in resistor networks.

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Detecting community structure in networks

More than 12 studies of different bottlenose dolphin populations, spanning from tropical to cold temperate waters, have shown that the species typically lives in societies in which relationships among individuals are predominantly fluid. In all cases dolphins lived in small groups characterised by fluid and dynamic interactions and some degree of dispersal from the natal group by both sexes. We describe a small, closed population of bottlenose dolphins living at the southern extreme of the species' range. Individuals live in large, mixed-sex groups in which no permanent emigration/immigration has been observed over the past 7 years. All members within the community are relatively closely associated (average half-weight index>0.4). Both male–male and female–female networks of preferred associates are present, as are long-lasting associations across sexes. The community structure is temporally stable, compared to other bottlenose dolphin populations, and constant companionship seems to be prevalent in the temporal association pattern. Such high degrees of stability are unprecedented in studies of bottlenose dolphins and may be related to the ecological constraints of Doubtful Sound. Fjords are low-productivity systems in which survival may easily require a greater level of co-operation, and hence group stability. These conditions are also present in other cetacean populations forming stable groups. We therefore hypothesise that ecological constraints are important factors shaping social interactions within cetacean societies.

The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations

Dolphins and porpoises in coastal and/or riverine habitats face serious conservation threats, yet surveys of their abundance are often especially difficult due to the challenges imposed by the habitats. Because many of these species occur in developing countries, lack of resources imposes a further set of challenges. 2. We offer advice on designing and conducting line-transect surveys with a focus on sound, practical, design rather than analytical sophistication, and we attempt, where possible, to offer simple, inexpensive solutions. 3. We guide the reader through the questions of what kind of survey should be done, whether by boat or aircraft, and we discuss ways to avoid bias and increase precision. 4. Our treatment of field methods focuses especially on robust, but low-cost, approaches. We provide two case studies to illustrate the implementation of these ideas.

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Design and field methods for sighting surveys of cetaceans in coastal and riverine habitats

Summary 1. Marine protected areas (MPAs) have been advocated for the protection of threatened marine mammals, but there is no empirical evidence that they are effective. In 1988, the Banks Peninsula Marine Mammal Sanctuary was established to reduce gillnet mortalities of Hector’s dolphin Cephalorhynchus hectori, an endangered dolphin species endemic to New Zealand. This study assesses the effectiveness of the MPA in improving the survival rate of Hector’s dolphin at Banks Peninsula. 2. Over 21 years, we undertook photo-identification surveys of Hector’s dolphins along standardized transects from small outboard-powered boats. From 1986 to 2006, we photographically captured 462 reliably marked individuals. We estimated mean annual survival during the pre-sanctuary and post-sanctuary periods by applying a Bayesian random effects capture-recapture model to the data. Population growth was estimated from population simulations using a stage-structured matrix model. 3. We estimate a 90% probability that survival has improved between the pre-sanctuary and postsanctuary periods, with estimates of mean survival probability increasing by 5AE4% (from 0AE863 to 0AE917). This improvement in survival corresponds to a 6% increase in mean annual population growth (from 0AE939 to 0AE995). 4. Synthesis and applications. Our study demonstrates improvement in a demographic parameter of an endangered marine mammal species following conservation action. Our results provide evidence that area-based protection measures can be effective for marine mammals. We note that estimating demographic parameters in marine mammals requires many years of data to achieve sufficient precision to detect biologically meaningful change. MPAs should be established with a commitment to long-term monitoring.

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First evidence that marine protected areas can work for marine mammals

Active sound emitters ('pingers') are used in several gillnet fisheries to reduce bycatch of small cetaceans, and/or to reduce depredation by dolphins. Here, we review studies conducted to determine how effective these devices may be as management tools. Significant reductions in bycatch of harbour porpoise Phocoena phocoena, franciscana Pontoporia blainvillei, common Delphinus delphis and striped dolphin Stenella coeruleoalba, and beaked whales as a group have been demonstrated. For harbour porpoise this result has been replicated in 14 con- trolled experiments in North America and Europe, and appears to be due to porpoises avoiding the area ensonified by pingers. Two gillnet fisheries (California-Oregon driftnet fishery for sword- fish; New England groundfish fishery) with mandatory pinger use have been studied for over a decade. Bycatch rates of dolphins/porpoises have fallen by 50 to 60%, and there is no evidence of bycatch increasing over time due to habituation. In both fisheries, bycatch rates were significantly higher in nets sparsely equipped with pingers or in which pingers had failed, than in nets without any pingers at all. Studies of pinger use to reduce depredation by bottlenose dolphins Tursiops truncatus generally show small and inconsistent improvements in fish catches and somewhat reduced net damage. Dolphin bycatch in these fisheries is rare, but still occurs in nets with pingers. Taken together, these studies suggest that the most promising candidates for bycatch reduction via pinger use will be gillnet fisheries in developed countries in which the bycaught cetaceans are generally neophobic species with large home ranges. We offer a set of lessons learned from the last decade of bycatch management.

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To ping or not to ping: the use of active acoustic devices in mitigating interactions between small cetaceans and gillnet fisheries

Knowledge about home ranges is essential for understanding the resources required by a species, identifying critical habitats, and revealing the overlap with anthropogenic impacts. Ranging behavior of Hector's dolphins (Cepbalorhyncbus bectori) was studied via coastal photo-ID surveys in the Banks Peninsula Marine Mammal Sanctuary (BPMMS) between 1985 and 2006. Univariate kernel density estimates of alongshore home range were calculated for 20 individuals with 15 sightings or more. For each individual, sighting locations were transformed into a univariate data set by projecting sightings onto a line drawn 1 km from the coast and measuring the distance along this line relative to an origin. Sightings were weighted by survey effort. Ninety-five percent (K 95 ) of the density estimate was used as a measure of alongshore home range, and 50% of the estimate (K 50 ) was used to reveal core portions of coastline where dolphins concentrated their activity. The mean estimates of K 95 and K 50 were 49.69 km (SE = 5.29) and 17.13 km (SE = 1.89), respectively. Four distinct hubs were apparent where the core areas of different individuals coincided. Three of the dolphins' alongshore ranges extended beyond the current northern boundary of the BPMMS, raising fresh concerns that the sanctuary is not large enough. Proposed changes to gill netting regulations, if enacted, will result in the alongshore ranges of all the dolphins in our study being protected.

Steve Dawson

Papers

The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations

Design and field methods for sighting surveys of cetaceans in coastal and riverine habitats

First evidence that marine protected areas can work for marine mammals

To ping or not to ping: the use of active acoustic devices in mitigating interactions between small cetaceans and gillnet fisheries

Kernel density estimates of alongshore home range of Hector's dolphins at Banks Peninsula, New Zealand