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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…
Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…
Across income groups and countries, individual citizens perceive economic inequality spectacularly wrong. These misperceptions have far-reaching consequences, as it is perceived inequality, not actualinequality informing redistributive…
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…
Most empirical studies of networks assume that the network data we are given represent a complete and accurate picture of the nodes and edges in the system of interest, but in real-world situations this is rarely the case. More often the…
Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the…
In this paper we quantify our limited information horizon, by measuring the information necessary to locate specific nodes in a network. To investigate different ways to overcome this horizon, and the interplay between communication and…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
Numerous networked systems feature a structure of nontrivial communities, which often correspond to their functional modules. Such communities have been detected in real-world biological, social and technological systems, as well as in…
We consider the problem of selecting a minimum size subset of nodes in a network, that allows to activate all the nodes of the network. We present a fast and simple algorithm that, in real-life networks, produces solutions that outperform…
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We…
Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial networks can be well-represented by geometry of negative…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
This paper aims to measure the efficiency of urban street networks (a kind of complex networks) from the perspective of the multidimensional chain of connectivity (or flow). More specifically, we define two quantities: flow dimension and…
The investigation of social networks is often hindered by their size as such networks often consist of at least thousands of vertices and edges. Hence, it is of major interest to derive compact structures that represent important…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…