Understanding the complex dynamics of communities of software developers requires a view of such organizations as a network of interacting agents involving both goals and constraints. Beyond their special features, these systems display some overall patterns of organization not far from the ones seen in other types of organizations, including both natural and artificial entities. By looking at both software developers and social insects as agents interacting in a complex network, we found common statistical patterns of organization. Here, simple self-organizing processes leading to the formation of hierarchies in wasp colonies and open source communities are studied. Our analysis further validates simple models of formation of wasp hierarchies based on individual learning. In the open source community, a few members are clearly distinguished from the rest of the community with different reinforcement mechanisms.
A co-authorship network of scientists at a university is an archetypical example of a complex evolving network. Collaborative R&D networks are self-organized products of partner choice between scientists. Modern science is, due to the immanent imperative of newness, strongly interdisciplinary. Crossovers between the different scientific disciplines and organizational units are observable on a daily basis. Since collaborative research has become the dominant and most promising way to produce high-quality output, collaboration structures are also a target for research and management design. We s…
In network science, a group of nodes connected with each other at higher probability than with those outside the group is referred to as a community. From the perspective that individual communities are associated with functional modules constituting complex systems described by networks, discovering communities is primarily important for understanding overall functions of these systems. Much effort has been devoted to developing methods to detect communities in networks since the early days of network science. Nevertheless, the method to reveal key characteristics of communities in real-world…
Among topics of opinion formation it is of interest to observe the characteristics of networks with a priori distinct communities. As an illustration, we report on the citation network(s) unfolded in the recent decades through web available works belonging to selected members of the Neocreationist and Intelligent Design Proponents (IDP) and the Darwinian Evolution Defenders (DED) communities. An adjacency matrix of tagged nodes is first constructed; it is not symmetric. A generalization of considerations pertaining to the case of networks with biased links, directed or undirected, is thus pres…
Weaker Coherence, Weaker Reciprocity: Comparing the Semantic and Social Organization of Moltbook and Reddit
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales（布宜诺斯艾利斯大学，理学院）；Instituto de Física Interdisciplinaria y Aplicada (INFINA), CONICET – Universidad de Buenos Aires（跨学科与应用物理研究所 (INFINA)，阿根廷国家科学研究委员会 - 布宜诺斯艾利斯大学）；Instituto Balseiro, Universidad Nacional de Cuyo y Comisión Nacional de Energía Atómica（巴尔塞罗研究所，门多萨国立大学与阿根廷国家原子能委员会）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（阿根廷国家科学研究委员会 (CONICET)）
Social networks are typical attributed networks with node attributes. Different from traditional attribute community detection problem aiming at obtaining the whole set of communities in the network, we study an application-oriented problem of mining an application-aware community organization with respect to specific concerned attributes. The concerned attributes are designated based on the requirements of any application by a user in advance. The application-aware community organization w.r.t. concerned attributes consists of the communities with feature subspaces containing these concerned …
Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of networks is to identify communities: groups of related nodes that correspond to functional subunits such as protein complexes or social spheres. Communities in networks often overlap such that nodes simultaneously belong to several groups. Meanwhile, many networks are known to possess hierarchical organization, where communities are recursively grouped into a hi…
We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.
Social networks where the actors occupy geospatial locations are prevalent in military, intelligence, and policing operations such as counter-terrorism, counter-insurgency, and combating organized crime. These networks are often derived from a variety of intelligence sources. The discovery of communities that are geographically disperse stems from the requirement to identify higher-level organizational structures, such as a logistics group that provides support to various geographically disperse terrorist cells. We apply a variant of Newman-Girvan modularity to this problem known as distance m…
We investigate the community structure of the global ownership network of transnational corporations. We find a pronounced organization in communities that cannot be explained by randomness. Despite the global character of this network, communities reflect first of all the geographical location of firms, while the industrial sector plays only a marginal role. We also analyze the network in which the nodes are the communities and the links are obtained by aggregating the links among firms belonging to pairs of communities. We analyze the network centrality of the top 50 communities and we provi…
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null random graph model. Here we introduce a systematic dynamical framework to design and analyze a wide variety of quality functions for community detection. The quality of a partition is measured by its Markov Stability, a time-parametrized function defined in terms of the statistical properties of a Markov process taking place on the graph. The Markov process pr…
Community discovery in complex networks is an interesting problem with a number of applications, especially in the knowledge extraction task in social and information networks. However, many large networks often lack a particular community organization at a global level. In these cases, traditional graph partitioning algorithms fail to let the latent knowledge embedded in modular structure emerge, because they impose a top-down global view of a network. We propose here a simple local-first approach to community discovery, able to unveil the modular organization of real complex networks. This i…
Identification of communities in complex networks has become an effective means to analysis of complex systems. It has broad applications in diverse areas such as social science, engineering, biology and medicine. Finding communities of nodes and finding communities of links are two popular schemes for network structure analysis. These schemes, however, have inherent drawbacks and are often inadequate to properly capture complex organizational structures in real networks. We introduce a new scheme and effective approach for identifying complex network structures using a mixture of node and lin…
What defines a group of friends? Rethinking community structure in signed, directed networks
Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid（马德里卡洛斯三世大学复杂系统跨学科小组数学系）；Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza（萨拉戈萨大学生物计算与复杂系统物理研究所）；Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington（印第安纳大学布鲁明顿分校卢迪信息、计算与工程学院复杂网络与系统研究中心）
The hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The Popularity-Similarity-Optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, reproducing strong clustering and scale-free degree distribution, however it misses to reproduce an important feature of real complex networks, which is the community organization. The Geometrical-Preferential-Attachment (GPA) model was…
Researchers use community-detection algorithms to reveal large-scale organization in biological and social networks, but community detection is useful only if the communities are significant and not a result of noisy data. To assess the statistical significance of the network communities, or the robustness of the detected structure, one approach is to perturb the network structure by removing links and measure how much the communities change. However, perturbing sparse networks is challenging because they are inherently sensitive; they shatter easily if links are removed. Here we propose a sim…
To understand the structure and organization of a large-scale social, biological or technological network, it can be helpful to describe and extract local communities or modules of the network. In this article, we develop a neurodynamic framework to describe the local communities which correspond to the stable states of a neuro-system built based on the network. The quantitative criteria to describe the neurodynamic system can cover a large range of objective functions. The resolution limit of these functions enable us to propose a generic criterion to explore multi-resolution local communitie…
We present a novel approach to partitioning network nodes into non-overlapping communities - a key step in revealing network modularity and hierarchical organization. Our methodology, applicable to networks with both weighted and unweighted symmetric edges, uses random walks to explore neighboring nodes in the same community. The walk-likelihood algorithm (WLA) produces an optimal partition of network nodes into a given number of communities. The walk-likelihood community finder (WLCF) employs WLA to predict both the optimal number of communities and the corresponding network partition. We hav…
Diffusion-driven pattern formation in an opinion dynamical network model
Helmholtz Institute for Functional Marine Biodiversity (HIFMB)（赫尔姆霍兹功能海洋生物多样性研究所）；Carl-von-Ossietzky University, Institute for Chemistry and Biology of the Marine Environment（卡尔·冯·奥西茨基大学，海洋环境化学与生物学研究所）；Alfred-Wegener Institute (AWI), Helmholtz Center for Polar and Marine Research（阿尔弗雷德·魏格纳研究所（AWI），赫尔姆霍兹极地海洋研究中心）
We propose a simple probabilistic model to explain the spatial structure of the rent distribution of housing market in city of Sapporo. Here we modify the mathematical model proposed by Gauvin et. al. Especially, we consider the competition between two distances, namely, the distance between house and center, and the distance between house and office. Computer simulations are carried out to reveal the self-organized spatial structure appearing in the rent distribution. We also compare the resulting distribution with empirical rent distribution in Sapporo as an example of cities designated by o…
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 …
Most of the complex social, technological and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored small-world and scale-free properties of these networks. Despite the large interest in characterizing the community structures of real networks, not enough attention has been devoted to the detection of universal mechanisms able to spontaneously generate networks with communities. Triadic closure is a natural mechanism to make new connections, especially in so…
Network analysis is becoming increasingly relevant in the historical investigation of scientific communities and their knowledge circulation process, because it offers the opportunity to explore and visualize connections amog scientific actors on a scale qualitatively different from traditional historical methods. Temporal networks are especially suitable for this task, as they allow to investigate the evolution of scientific communities over time. In this paper we will rely on the analytical tools provided by temporal networks to examine the technical comission on agriculture (1913 - 1947) es…
Community detection algorithms are fundamental tools that allow us to uncover organizational principles in networks. When detecting communities, there are two possible sources of information one can use: the network structure, and the features and attributes of nodes. Even though communities form around nodes that have common edges and common attributes, typically, algorithms have only focused on one of these two data modalities: community detection algorithms traditionally focus only on the network structure, while clustering algorithms mostly consider only node attributes. In this paper, we …
Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical levels, where the clusters defined at one level appear as elementary entities at the next higher level. Using a simple model of a hierarchical modular network, we show that such a topological structure gives rise to characteristic time-scale separation between dynamics occurring at different levels of the hierarchy. This generalizes our earlier result for sim…
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 heterogenous distributions of node degree and community size. An increasing attention has been recently d…
Network communities represent mesoscopic structure for understanding the organization of real-world networks, where nodes often belong to multiple communities and form overlapping community structure in the network. Due to non-triviality in finding the exact boundary of such overlapping communities, this problem has become challenging, and therefore huge effort has been devoted to detect overlapping communities from the network. In this paper, we present PVOC (Permanence based Vertex-replication algorithm for Overlapping Community detection), a two-stage framework to detect overlapping communi…
Community detection algorithms are fundamental tools to understand organizational principles in social networks. With the increasing power of social media platforms, when detecting communities there are two possi- ble sources of information one can use: the structure of social network and node attributes. However structure of social networks and node attributes are often interpreted separately in the research of community detection. When these two sources are interpreted simultaneously, one common as- sumption shared by previous studies is that nodes attributes are correlated with communities.…
Business elites reconfigure their locus of organization over time, from the city level, to the national level, and beyond. We ask what the current level of elite organization is and propose a novel theoretical and empirical approach to answer this question. Building on the universal distinction between local and nonlocal ties we use network analysis and community detection to dissect the global network of interlocking directorates among over five million firms. We find that elite orientation is indeed changing from the national to the transnational plane, but we register a considerable heterog…
Inter-firm organizations, which play a driving role in the economy of a country, can be represented in the form of a customer-supplier network. Such a network exhibits a heavy-tailed degree distribution, disassortative mixing and a prominent community structure. We analyze a large-scale data set of customer-supplier relationships containing data from one million Japanese firms. Using a directed network framework, we show that the production network exhibits the characteristics listed above. We conduct detailed investigations to characterize the communities in the network. The topology within s…
To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving network structure remains a challenging problem. Here we overcome this difficulty by combining the visual pattern recognition ability of humans with the high processing speed of computers to develop an exploratory method for discovering groups of nodes characterized by common network properties, including but not limited to communities of densely connected no…
Nestedness has traditionally been used to detect assembly patterns in meta-communities and networks of interacting species. Attempts have also been made to uncover nested structures in international trade, typically represented as bipartite networks in which connections can be established between countries (exporters or importers) and industries. A bipartite representation of trade, however, inevitably neglects transactions between industries. To fully capture the organization of the global value chain, we draw on the World Input-Output Database and construct a multi-layer network in which the…
Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and comm…
By mapping the most advanced elements of the contemporary social interactions, the world scientific collaboration network develops an extremely involved and heterogeneous organization. Selected characteristics of this heterogeneity are studied here and identified by focusing on the scientific collaboration community of H. Eugene Stanley - one of the most prolific world scholars at the present time. Based on the Web of Science records as of March 28, 2016, several variants of networks are constructed. It is found that the Stanley #1 network - this in analogy to the Erdős # - develops a largely …
Community Detection with the Map Equation and Infomap: Theory and Applications
IceLab, Department of Physics, Umeå University（于默奥大学物理系冰实验室）；Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade（贝尔格莱德大学贝尔格莱德物理研究所复杂系统研究中心科学计算实验室）
Networks are a natural and popular mechanism for the representation and investigation of a broad class of systems. But extracting information from a network can present significant challenges. We present NetzCope, a software application for the display and analysis of networks. Its key features include the visualization of networks in two or three dimensions, the organization of vertices to reveal structural similarity, and the detection and visualization of network communities by modularity maximization.
Revealing the community structure exhibited by real networks is a fundamental phase towards a comprehensive understanding of complex systems beyond the local organization of their components. Community detection techniques help on providing insights into understanding the local organization of the components of networks. In this study we identify and investigate the overlapping community structure of an interesting and unique case of study: the Estonian network of payments. In order to perform the study, we use the Clique Percolation Method and explore statistical distribution functions of the…
The mechanisms responsible for contention of activity in systems represented by networks are crucial in various phenomena, as in diseases such as epilepsy that affects the neuronal networks, and for information dissemination in social networks. The first models to account for contained activity included triggering and inhibition processes, but they cannot be applied to social networks where inhibition is clearly absent. A recent model showed that contained activity can be achieved with no need of inhibition processes provided that the network is subdivided in modules (communities). In this pap…
Detecting the time evolution of the community structure of networks is crucial to identify major changes in the internal organization of many complex systems, which may undergo important endogenous or exogenous events. This analysis can be done in two ways: considering each snapshot as an independent community detection problem or taking into account the whole evolution of the network. In the first case, one can apply static methods on the temporal snapshots, which correspond to configurations of the system in short time windows, and match afterwards the communities across layers. Alternativel…
Understanding social dynamics that govern human phenomena, such as communications and social relationships is a major problem in current computational social sciences. In particular, given the unprecedented success of online social networks (OSNs), in this paper we are concerned with the analysis of aggregation patterns and social dynamics occurring among users of the largest OSN as the date: Facebook. In detail, we discuss the mesoscopic features of the community structure of this network, considering the perspective of the communities, which has not yet been studied on such a large scale. To…
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the 'Markov stability' method of network community detection). Our approach captures variation of modular organization across different system states, time scales, a…
