Related papers: Distance Distribution in Extreme Modular Networks

Diffusion and propagation of information, influence and diseases take place over increasingly larger networks. We observe when a node copies information, makes a decision or becomes infected but networks are often hidden or unobserved.…

Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have…

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…

Inspired from human cognition, machine learning systems are gradually revealing advantages of sparser and more modular architectures. Recent work demonstrates that not only do some modular architectures generalize well, but they also lead…

Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time…

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…

To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…

Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively…

Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the…

In this paper we study a simple cascading process in a structured heterogeneous population, namely, a network composed of two loosely coupled communities. We demonstrate that under certain conditions the cascading dynamics in such a network…

Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…

In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…

We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…

Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community…

Modularity is a general principle present in many fields. It offers attractive advantages, including, among others, ease of conceptualization, interpretability, scalability, module combinability, and module reusability. The deep learning…

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,…