Concept associations can be represented by a network that consists of a set of nodes representing concepts and a set of edges representing their relationships. Complex networks exhibit some common topological features including small diameter, high degree of clustering, power-law degree distribution, and modularity. We investigated the topological properties of a network constructed from co-occurrences between MeSH descriptors in the MEDLINE database. We conducted the analysis on two networks, one constructed from all MeSH descriptors and another using only major descriptors. Network reduction was performed using the Pearson%s chi-square test for independence. To characterize topological properties of the network we adopted some specific measures, including diameter, average path length, clustering coefficient, and degree distribution. For the full MeSH network the average path length was 1.95 with a diameter of three edges and clustering coefficient of 0.26. The Kolmogorov-Smirnov test rejects the power law as a plausible model for degree distribution. For the major MeSH network the average path length was 2.63 edges with a diameter of seven edges and clustering coefficient of 0.15. The Kolmogorov-Smirnov test failed to reject the power law as a plausible model. The power-law exponent was 5.07. In both networks it was evident that nodes with a lower degree exhibit higher clustering than those with a higher degree. After simulated attack, where we removed 10% of nodes with the highest degrees, the giant component of each of the two networks contains about 90% of all nodes. Because of small average path length and high degree of clustering the MeSH network is small-world. A power-law distribution is not a plausible model for the degree distribution. The network is highly modular, highly resistant to targeted and random attack and with minimal dissortativity.

COBISS.SI-ID: 2048311059

Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network%s structure and also provide a clear real-world interpretation. Given this insight, we develop a framework for analysing and comparing networks, which outperforms all existing ones. We demonstrate its strength by uncovering novel relationships between seemingly unrelated networks, such as Facebook, metabolic, and protein structure networks. We also use it to track the dynamics of the world trade network, showing that a countrys role of a broker between non-trading countries indicates economic prosperity, whereas peripheral roles are associated with poverty. This result, though intuitive, has escaped all existing frameworks. Finally, our approach translates network topology into everyday language, bringing network analysis closer to domain scientists.

COBISS.SI-ID: 2048292371

Interaction among the scientific disciplines is of vital importance in modern science. Focusing on the case of Slovenia, we study the dynamics of interdisciplinary sciences from 1960 to 2010. Our approach relies on quantifying the interdisciplinarity of research communities detected in the coauthorship network of Slovenian scientists over time. Examining the evolution of the community structure, we find that the frequency of interdisciplinary research is only proportional with the overall growth of the network. Although marginal improvements in favor of interdisciplinarity are inferable during the 70s and 80s, the overall trends during the past 20 years are constant and indicative of stalemate. We conclude that the flow of knowledge between different fields of research in Slovenia is in need of further stimulation.

COBISS.SI-ID: 20503816

The coloring of disk graphs is motivated by the frequency assignment problem. In 1998, Malesinska et al. introduced double disk graphs as their generalization. They showed that the chromatic number of a double disk graph G is at most 33 D(G) - 35, where D(G) denotes the size of a maximum clique in G. Du et al. improved the upper bound to 31 D(G)-1. In this paper we decrease the bound substantially; namely we show that the chromatic number of G is at most 15 D(G) - 14.

COBISS.SI-ID: 2048330259

Motivated by questions about square-free monomial ideals in polynomial rings, C. A. Francisco et al. [Discrete Math. 310, No. 15--16, 2176--2182 (2010)] conjectured that for every positive integer $k$ and every $k$-critical (i.e., critically $k$-chromatic) graph, there is a set of vertices whose replication produces a ($k+1$)-critical graph. (The replication of a set $W$ of vertices of a graph is the operation that adds a copy of each vertex $w$ in $W$, one at a time, and connects it to $w$ and all its neighbours.) We disprove the conjecture by providing an infinite family of counterexamples. Furthermore, the smallest member of the family answers a question of Herzog and Hibi concerning the depth functions of square-free monomial ideals in polynomial rings, and a related question on the persistence property of such ideals.

COBISS.SI-ID: 16920665