To find interesting structure in networks, community detection algorithms have to take into account not only the network topology, but also dynamics of interactions between nodes. We investigate this claim using the paradigm of synchronization in a network of coupled oscillators. As the network evolves to a global steady state, nodes belonging to the same community synchronize faster than nodes belonging to different communities. Traditionally, nodes in network synchronization models are coupled via one-to-one, or conservative interactions. However, social interactions are often one-to-many, as for example, in social media, where users broadcast messages to all their followers. We formulate a novel model of synchronization in a network of coupled oscillators in which the oscillators are coupled via one-to-many, or non-conservative interactions. We study the dynamics of different interaction models and contrast their spectral properties. To find multi-scale community structure in a network of interacting nodes, we define a similarity function that measures the degree to which nodes are synchronized and use it to hierarchically cluster nodes. We study real-world social networks, including networks of two social media providers. To evaluate the quality of the discovered communities in a social media network we propose a community quality metric based on user activity. We find that conservative and non-conservative interaction models lead to dramatically different views of community structure even within the same network. Our work offers a novel mathematical framework for exploring the relationship between network structure, topology and dynamics.
Community detection methods are used to reveal the structure of complex networks. @cite_5 found core and whiskers' structure of real-world networks using conductance-based methods and argued that these methods cannot reveal any further structure in the giant core. Song @cite_17 claimed that there exist self-repeating patterns in complex networks at all length scales. Our results corroborate this claim, as we show a repeating core and whiskers' pattern in the Digg social network at many different length scales.
@cite_5 @cite_17
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Repetition is a core principle in music. Many musical pieces are characterized by an underlying repeating structure over which varying elements are superimposed. This is especially true for pop songs where a singer often overlays varying vocals on a repeating accompaniment. On this basis, we present the REpeating Pattern Extraction Technique (REPET), a novel and simple approach for separating the repeating “background” from the non-repeating “foreground” in a mixture. The basic idea is to identify the periodically repeating segments in the audio, compare them to a repeating segment model derived from them, and extract the repeating patterns via time-frequency masking. Experiments on data sets of 1,000 song clips and 14 full-track real-world songs showed that this method can be successfully applied for music voice separation, competing with two recent state-of-the-art approaches. Further experiments showed that REPET can also be used as a preprocessor to pitch detection algorithms to improve melody extraction. Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both unweighted and weighted scale free networks having local and global core-periphery as well as community structure. Network evolves using topological growth, self growth, and weight distribution function. To validate the correctness of proposed models, we use K-shell and S-shell decomposition methods. Simulation results show that the generated unweighted networks follow power law degree distribution with droop head and heavy tail. Similarly, generated weighted networks follow degree, strength, and edge-weight power law distributions. We further study other properties of complex networks, such as clustering coefficient, nearest neighbor degree, and strength degree correlation. Understanding of the mechanisms driving our daily face-to-face encounters is still limited; the field lacks large-scale datasets describing both individual behaviors and their collective interactions. However, here, with the help of travel smart card data, we uncover such encounter mechanisms and structures by constructing a time-resolved in-vehicle social encounter network on public buses in a city (about 5 million residents). Using a population scale dataset, we find physical encounters display reproducible temporal patterns, indicating that repeated encounters are regular and identical. On an individual scale, we find that collective regularities dominate distinct encounters’ bounded nature. An individual’s encounter capability is rooted in his her daily behavioral regularity, explaining the emergence of “familiar strangers” in daily life. Strikingly, we find individuals with repeated encounters are not grouped into small communities, but become strongly connected over time, resulting in a large, but imperceptible, small-world contact network or “structure of co-presence” across the whole metropolitan area. Revealing the encounter pattern and identifying this large-scale contact network are crucial to understanding the dynamics in patterns of social acquaintances, collective human behaviors, and—particularly—disclosing the impact of human behavior on various diffusion spreading processes. Networks provide a powerful way to study complex systems of interacting objects. Detecting network communities—groups of objects that often correspond to functional modules—is crucial to understanding social, technological, and biological systems. Revealing communities allows for analysis of system properties that are invisible when considering only individual objects or the entire system, such as the identification of module boundaries and relationships or the classification of objects according to their functional roles. However, in networks where objects can simultaneously belong to multiple modules at once, the decomposition of a network into overlapping communities remains a challenge. Here we present a new paradigm for uncovering the modular structure of complex networks, based on a decomposition of a network into any combination of overlapping, nonoverlapping, and hierarchically organized communities. We demonstrate on a diverse set of networks coming from a wide range of domains that our approach leads to more accurate communities and improved identification of community boundaries. We also unify two fundamental organizing principles of complex networks: the modularity of communities and the commonly observed core–periphery structure. We show that dense network cores form as an intersection of many overlapping communities. We discover that communities in social, information, and food web networks have a single central dominant core while communities in protein–protein interaction (PPI) as well as product copurchasing networks have small overlaps and form many local cores.