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Community structure is one of the most important features of complex networks. Modularity-based methods for community detection typically rely on heuristic algorithms to optimize a specific community quality function. Such methods are…
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…
Discovering community structure in complex networks is a mature field since a tremendous number of community detection methods have been introduced in the literature. Nevertheless, it is still very challenging for practioners to determine…
A wide array of complex biological, social, and physical systems have recently been shown to be quantitatively described by Ising models, which lie at the intersection of statistical physics and machine learning. Here, we study the…
The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
This paper considers the problem of algorithm selection for community detection. The aim of community detection is to identify sets of nodes in a network which are more interconnected relative to their connectivity to the rest of the…
The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community…
Understanding the structure of communities in a network has a great importance in the economic analysis. Communities are indeed characterized by specific properties, that are different from those of both the individual node and the whole…
This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a…
We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the…
Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. Moreover, many machine learning algorithms and…
Community detection refers to the problem of clustering the nodes of a network into groups. Existing inferential methods for community structure mainly focus on unweighted (binary) networks. Many real-world networks are nonetheless weighted…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…
How complex is an Ising model? Usually, this is measured by the computational complexity of its ground state energy problem. Yet, this complexity measure only distinguishes between planar and non-planar interaction graphs, and thus fails to…
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…