78,087 research outputs found
Clustering in Complex Directed Networks
Many empirical networks display an inherent tendency to cluster, i.e. to form
circles of connected nodes. This feature is typically measured by the
clustering coefficient (CC). The CC, originally introduced for binary,
undirected graphs, has been recently generalized to weighted, undirected
networks. Here we extend the CC to the case of (binary and weighted) directed
networks and we compute its expected value for random graphs. We distinguish
between CCs that count all directed triangles in the graph (independently of
the direction of their edges) and CCs that only consider particular types of
directed triangles (e.g., cycles). The main concepts are illustrated by
employing empirical data on world-trade flows
Empirical analysis of the ship-transport network of China
Structural properties of the ship-transport network of China (STNC) are
studied in the light of recent investigations of complex networks. STNC is
composed of a set of routes and ports located along the sea or river. Network
properties including the degree distribution, degree correlations, clustering,
shortest path length, centrality and betweenness are studied in different
definition of network topology. It is found that geographical constraint plays
an important role in the network topology of STNC. We also study the traffic
flow of STNC based on the weighted network representation, and demonstrate the
weight distribution can be described by power law or exponential function
depending on the assumed definition of network topology. Other features related
to STNC are also investigated.Comment: 20 pages, 7 figures, 1 tabl
Comparison of the language networks from literature and blogs
In this paper we present the comparison of the linguistic networks from
literature and blog texts. The linguistic networks are constructed from texts
as directed and weighted co-occurrence networks of words. Words are nodes and
links are established between two nodes if they are directly co-occurring
within the sentence. The comparison of the networks structure is performed at
global level (network) in terms of: average node degree, average shortest path
length, diameter, clustering coefficient, density and number of components.
Furthermore, we perform analysis on the local level (node) by comparing the
rank plots of in and out degree, strength and selectivity. The
selectivity-based results point out that there are differences between the
structure of the networks constructed from literature and blogs
The multiplex structure of interbank networks
The interbank market has a natural multiplex network representation. We
employ a unique database of supervisory reports of Italian banks to the Banca
d'Italia that includes all bilateral exposures broken down by maturity and by
the secured and unsecured nature of the contract. We find that layers have
different topological properties and persistence over time. The presence of a
link in a layer is not a good predictor of the presence of the same link in
other layers. Maximum entropy models reveal different unexpected substructures,
such as network motifs, in different layers. Using the total interbank network
or focusing on a specific layer as representative of the other layers provides
a poor representation of interlinkages in the interbank market and could lead
to biased estimation of systemic risk.Comment: 41 pages, 8 figures, 10 table
A New Methodology for Generalizing Unweighted Network Measures
Several important complex network measures that helped discovering common
patterns across real-world networks ignore edge weights, an important
information in real-world networks. We propose a new methodology for
generalizing measures of unweighted networks through a generalization of the
cardinality concept of a set of weights. The key observation here is that many
measures of unweighted networks use the cardinality (the size) of some subset
of edges in their computation. For example, the node degree is the number of
edges incident to a node. We define the effective cardinality, a new metric
that quantifies how many edges are effectively being used, assuming that an
edge's weight reflects the amount of interaction across that edge. We prove
that a generalized measure, using our method, reduces to the original
unweighted measure if there is no disparity between weights, which ensures that
the laws that govern the original unweighted measure will also govern the
generalized measure when the weights are equal. We also prove that our
generalization ensures a partial ordering (among sets of weighted edges) that
is consistent with the original unweighted measure, unlike previously developed
generalizations. We illustrate the applicability of our method by generalizing
four unweighted network measures. As a case study, we analyze four real-world
weighted networks using our generalized degree and clustering coefficient. The
analysis shows that the generalized degree distribution is consistent with the
power-law hypothesis but with steeper decline and that there is a common
pattern governing the ratio between the generalized degree and the traditional
degree. The analysis also shows that nodes with more uniform weights tend to
cluster with nodes that also have more uniform weights among themselves.Comment: 23 pages, 10 figure
On the Topological Properties of the World Trade Web: A Weighted Network Analysis
This paper studies the topological properties of the World Trade Web (WTW)
and its evolution over time by employing a weighted network analysis. We show
that the WTW, viewed as a weighted network, displays statistical features that
are very different from those obtained by using a traditional binary-network
approach. In particular, we find that: (i) the majority of existing links are
associated to weak trade relationships; (ii) the weighted WTW is only weakly
disassortative; (iii) countries holding more intense trade relationships are
more clustered.Comment: To be submitted to APFA 6 Proceedings. 8 pages, 10 figure
Null Models of Economic Networks: The Case of the World Trade Web
In all empirical-network studies, the observed properties of economic
networks are informative only if compared with a well-defined null model that
can quantitatively predict the behavior of such properties in constrained
graphs. However, predictions of the available null-model methods can be derived
analytically only under assumptions (e.g., sparseness of the network) that are
unrealistic for most economic networks like the World Trade Web (WTW). In this
paper we study the evolution of the WTW using a recently-proposed family of
null network models. The method allows to analytically obtain the expected
value of any network statistic across the ensemble of networks that preserve on
average some local properties, and are otherwise fully random. We compare
expected and observed properties of the WTW in the period 1950-2000, when
either the expected number of trade partners or total country trade is kept
fixed and equal to observed quantities. We show that, in the binary WTW,
node-degree sequences are sufficient to explain higher-order network properties
such as disassortativity and clustering-degree correlation, especially in the
last part of the sample. Conversely, in the weighted WTW, the observed sequence
of total country imports and exports are not sufficient to predict higher-order
patterns of the WTW. We discuss some important implications of these findings
for international-trade models.Comment: 39 pages, 46 figures, 2 table
Correlation Between Student Collaboration Network Centrality and Academic Performance
We compute nodal centrality measures on the collaboration networks of
students enrolled in three upper-division physics courses, usually taken
sequentially, at the Colorado School of Mines. These are complex networks in
which links between students indicate assistance with homework. The courses
included in the study are intermediate Classical Mechanics, introductory
Quantum Mechanics, and intermediate Electromagnetism. By correlating these
nodal centrality measures with students' scores on homework and exams, we find
four centrality measures that correlate significantly with students' homework
scores in all three courses: in-strength, out-strength, closeness centrality,
and harmonic centrality. These correlations suggest that students who not only
collaborate often, but also collaborate significantly with many different
people tend to achieve higher grades. Centrality measures between simultaneous
collaboration networks (analytical vs. numerical homework collaboration)
composed of the same students also correlate with each other, suggesting that
students' collaboration strategies remain relatively stable when presented with
homework assignments targeting different skills. Additionally, we correlate
centrality measures between collaboration networks from different courses and
find that the four centrality measures with the strongest relationship to
students' homework scores are also the most stable measures across networks
involving different courses. Correlations of centrality measures with exam
scores were generally smaller than the correlations with homework scores,
though this finding varied across courses.Comment: 10 pages, 4 figures, submitted to Phys. Rev. PE
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