Author Correction: Genetic insights into the social organisation of the Avar period elite in the 7th century AD Carpathian Basin.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The role of detours in individual human navigation patterns of complex networks.

Despite its importance for public transportation, communication within organizations or the general understanding of organized knowledge, our understanding of how human individuals navigate complex networked systems is still limited owing to the lack of datasets recording a sufficient amount of navigation paths of individual humans. Here, we analyse 10587 paths recorded from 259 human subjects when navigating between nodes of a complex word-morph network. We find a clear presence of systematic detours organized around individual hierarchical scaffolds guiding navigation. Our dataset is the first enabling the visualization and analysis of scaffold hierarchies whose presence and role in supporting human navigation is assumed in existing navigational models. By using an information-theoretic argumentation, we argue that taking short detours following the hierarchical scaffolds is a clear sign of human subjects simplifying the interpretation of the complex networked system by an order of magnitude. We also discuss the role of these scaffolds in the phases of learning to navigate a network from scratch.

Genetic insights into the social organisation of the Avar period elite in the 7th century AD Carpathian Basin.

After 568 AD the Avars settled in the Carpathian Basin and founded the Avar Qaganate that was an important power in Central Europe until the 9th century. Part of the Avar society was probably of Asian origin; however, the localisation of their homeland is hampered by the scarcity of historical and archaeological data. Here, we study mitogenome and Y chromosomal variability of twenty-six individuals, a number of them representing a well-characterised elite group buried at the centre of the Carpathian Basin more than a century after the Avar conquest. The studied group has maternal and paternal genetic affinities to several ancient and modern East-Central Asian populations. The majority of the mitochondrial DNA variability represents Asian haplogroups (C, D, F, M, R, Y and Z). The Y-STR variability of the analysed elite males belongs only to five lineages, three N-Tat with mostly Asian parallels and two Q haplotypes. The homogeneity of the Y chromosomes reveals paternal kinship as a cohesive force in the organisation of the Avar elite strata on both social and territorial level. Our results indicate that the Avar elite arrived in the Carpathian Basin as a group of families, and remained mostly endogamous for several generations after the conquest.

A dataset on human navigation strategies in foreign networked systems.

Humans are involved in various real-life networked systems. The most obvious examples are social and collaboration networks but the language and the related mental lexicon they use, or the physical map of their territory can also be interpreted as networks. How do they find paths between endpoints in these networks? How do they obtain information about a foreign networked world they find themselves in, how they build mental model for it and how well they succeed in using it? Large, open datasets allowing the exploration of such questions are hard to find. Here we report a dataset collected by a smartphone application, in which players navigate between fixed length source and destination English words step-by-step by changing only one letter at a time. The paths reflect how the players master their navigation skills in such a foreign networked world. The dataset can be used in the study of human mental models for the world around us, or in a broader scope to investigate the navigation strategies in complex networked systems.

Routes Obey Hierarchy in Complex Networks.

The last two decades of network science have discovered stunning similarities in the topological characteristics of real life networks (many biological, social, transportation and organizational networks) on a strong empirical basis. However our knowledge about the operational paths used in these networks is very limited, which prohibits the proper understanding of the principles of their functioning. Today, the most widely adopted hypothesis about the structure of the operational paths is the shortest path assumption. Here we present a striking result that the paths in various networks are significantly stretched compared to their shortest counterparts. Stretch distributions are also found to be extremely similar. This phenomenon is empirically confirmed on four networks from diverse areas of life. We also identify the high-level path selection rules nature seems to use when picking its paths.

Geometric explanation of the rich-club phenomenon in complex networks.

The rich club organization (the presence of highly connected hub core in a network) influences many structural and functional characteristics of networks including topology, the efficiency of paths and distribution of load. Despite its major role, the literature contains only a very limited set of models capable of generating networks with realistic rich club structure. One possible reason is that the rich club organization is a divisive property among complex networks which exhibit great diversity, in contrast to other metrics (e.g. diameter, clustering or degree distribution) which seem to behave very similarly across many networks. Here we propose a simple yet powerful geometry-based growing model which can generate realistic complex networks with high rich club diversity by controlling a single geometric parameter. The growing model is validated against the Internet, protein-protein interaction, airport and power grid networks.

Navigable networks as Nash equilibria of navigation games.

Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.