The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which generalizes the hyper-network and hyper-structure models, fits perfectly with several real-life complex systems, including social and public transportation networks. We present an analysis of the structural properties of the multilevel network, including the clustering and the metric structures. Some analytical relationships amongst the efficiency and clustering coefficient of this new model and the corresponding parameters of the underlying network are obtained. Finally some random models for multilevel networks are given to illustrate how different multilevel structures can produce similar underlying networks and therefore that the mesoscale structure should be taken into account in many applications.
Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical net…
Uncovering structural properties of ecological networks is a crucial starting point of studying the system's stability in response to various types of perturbations. We analyze pollination and seed disposal networks, which are representative examples of mutualistic networks in ecosystems, in various scales. In particular, we examine mesoscale properties such as the nested structure, the core-periphery structure, and the community structure by statistically investigating their interrelationships with real network data. As a result of community detection in different scales, we find the absence …
When facing complex mesoscale network structures, it is generally believed that (null) models encoding the modular organization of nodes must be employed. The present paper focuses on two block structures that characterize the mesoscale organization of many real-world networks, i.e. the bow-tie and the core-periphery ones. Our analysis shows that constraining the network degree sequence is often enough to reproduce such structures, as confirmed by model selection criteria as AIC or BIC. As a byproduct, our paper enriches the toolbox for the analysis of bipartite networks - still far from being…
The importance of identifying the presence of mesoscale structures in complex networks can be hardly overestimated. So far, much attention has been devoted to the detection of communities, bipartite and core-periphery structures on binary networks: such an effort has led to the definition of a unified framework based upon the score function called surprise, i.e. a p-value that can be assigned to any given partition of nodes, on both undirected and directed networks. Here, we aim at making a step further, by extending the entire framework to the weighted case: after reviewing the application of…
University of Sydney（悉尼大学）；Goethe University Frankfurt（法兰克福歌德大学）；IT:U Interdisciplinary Transformation University（IT：U跨学科转型大学）；Central European University（中欧大学）；Complexity Science Hub（复杂性科学中心）
Generative models for two-ground-truth partitions in networks
Centre Marc Bloch（马克·布洛赫中心）；Centre national de la recherche scientifique (CNRS)（法国国家科学研究中心）；École des hautes études en sciences sociales (EHESS)（法国高等社会科学研究院）
Inference of Hierarchical Core-Periphery Structure in Temporal Networks
University of California, Los Angeles（加州大学洛杉矶分校）；University of Michigan（密歇根大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Uppsala University（乌普萨拉大学）；Santa Fe Institute（圣塔菲研究所）
Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e. groups of nodes whose connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite struc…
Princeton University（普林斯顿大学）；University of Hong Kong（香港大学）；University of Vermont（佛蒙特大学）；Grinnell College（格林内尔学院）；University of Oxford（牛津大学）；University of Virginia（弗吉尼亚大学）
Schizophrenia, a mental disorder that is characterized by abnormal social behavior and failure to distinguish one's own thoughts and ideas from reality, has been associated with structural abnormalities in the architecture of functional brain networks. Using various methods from network analysis, we examine the effect of two classical therapeutic antipsychotics --- Aripiprazole and Sulpiride --- on the structure of functional brain networks of healthy controls and patients who have been diagnosed with schizophrenia. We compare the community structures of functional brain networks of different …
