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A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level, scientists studied interdependent multilayer networks. In this letter, we introduce a new kind of interdependent multilayer networks, i.e., interconnecting networks, for which the component networks are coupled each other by sharing some common nodes. Based on the empirical investigations, we revealed a common feature of such interconnecting networks, namely, the networks with smaller averaged topological differences of the interconnecting nodes tend to share more nodes. A very simple node sharing mechanism is proposed to analytically explain the observed feature of the interconnecting networks.
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We present a model, in which some nodes (called interconnecting nodes) in two networks merge and play the roles in both the networks. The model analytic and simulation discussions show a monotonically increasing dependence of interconnecting node topological position difference and a monotonically decreasing dependence of the interconnecting node number on function difference of both networks. The dependence function details do not influence the qualitative relationship. This online manuscript presents the details of the model simulation and analytic discussion, as well as the empirical investigations performed in eight real world bilayer networks. The analytic and simulation results with different dependence function forms show rather good agreement with the empirical conclusions.
This manuscript serves as an online supplement of a preprint, which presents a study on a kind of bilayer networks where some nodes (called interconnecting nodes) in two layers merge. A model showing an important general property of the bilayer networks is proposed. Then the analytic discussion of the model is compared with empirical conclusions. We present all the empirical observations in this online supplement.
A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that real networks typically have more bridges than their completely randomized counterparts, but very similar fraction of bridges as their degree-preserving randomizations. We define a new edge centrality measure, called bridgeness, to quantify the importance of a bridge in damaging a network. We find that certain real networks have very large average and variance of bridgeness compared to their degree-preserving randomizations and other real networks. Finally, we offer an analytical framework to calculate the bridge fraction , the average and variance of bridgeness for uncorrelated random networks with arbitrary degree distributions.
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant advances in the understanding of the structure, formation and function of complex systems. Social and biological processes such as the dynamics of epidemics, the diffusion of information in social media, the interactions between species in ecosystems or the communication between neurons in our brains are all actively studied using dynamical models on complex networks. In all of these systems, the patterns of connections at the individual level play a fundamental role on the global dynamics and finding the most important nodes allows one to better understand and predict their behaviors. An important research effort in network science has therefore been dedicated to the development of methods allowing to find the most important nodes in networks. In this short entry, we describe network centrality measures based on the notions of network traversal they rely on. This entry aims at being an introduction to this extremely vast topic, with many contributions from several fields, and is by no means an exhaustive review of all the literature about network centralities.
Social network analysis tools can infer various attributes just by scrutinizing ones connections. Several researchers have studied the problem faced by an evader whose goal is to strategically rewire their social connections in order to mislead such tools, thereby concealing their private attributes. However, to date, this literature has only considered static networks, while neglecting the more general case of temporal networks, where the structure evolves over time. Driven by this observation, we study how the evader can conceal their importance from an adversary armed with temporal centrality measures. We consider computational and structural aspects of this problem: Is it computationally feasible to calculate optimal ways of hiding? If it is, what network characteristics facilitate hiding? This topic has been studied in static networks, but in this work, we add realism to the problem by considering temporal networks of edges changing in time. We find that it is usually computationally infeasible to find the optimal way of hiding. On the other hand, by manipulating ones contacts, one could add a surprising amount of privacy. Compared to static networks, temporal networks offer more strategies for this type of manipulation and are thus, to some extent, easier to hide in.
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