1,978 research outputs found
Second-Order Assortative Mixing in Social Networks
In a social network, the number of links of a node, or node degree, is often
assumed as a proxy for the node's importance or prominence within the network.
It is known that social networks exhibit the (first-order) assortative mixing,
i.e. if two nodes are connected, they tend to have similar node degrees,
suggesting that people tend to mix with those of comparable prominence. In this
paper, we report the second-order assortative mixing in social networks. If two
nodes are connected, we measure the degree correlation between their most
prominent neighbours, rather than between the two nodes themselves. We observe
very strong second-order assortative mixing in social networks, often
significantly stronger than the first-order assortative mixing. This suggests
that if two people interact in a social network, then the importance of the
most prominent person each knows is very likely to be the same. This is also
true if we measure the average prominence of neighbours of the two people. This
property is weaker or negative in non-social networks. We investigate a number
of possible explanations for this property. However, none of them was found to
provide an adequate explanation. We therefore conclude that second-order
assortative mixing is a new property of social networks.Comment: Cite as: Zhou S., Cox I.J., Hansen L.K. (2017) Second-Order
Assortative Mixing in Social Networks. In: Goncalves B., Menezes R., Sinatra
R., Zlatic V. (eds) Complex Networks VIII. CompleNet 2017. Springer
Proceedings in Complexity. Springer, Cham.
https://doi.org/10.1007/978-3-319-54241-6_
Structural efficiency of percolation landscapes in flow networks
Complex networks characterized by global transport processes rely on the
presence of directed paths from input to output nodes and edges, which organize
in characteristic linked components. The analysis of such network-spanning
structures in the framework of percolation theory, and in particular the key
role of edge interfaces bridging the communication between core and periphery,
allow us to shed light on the structural properties of real and theoretical
flow networks, and to define criteria and quantities to characterize their
efficiency at the interplay between structure and functionality. In particular,
it is possible to assess that an optimal flow network should look like a "hairy
ball", so to minimize bottleneck effects and the sensitivity to failures.
Moreover, the thorough analysis of two real networks, the Internet
customer-provider set of relationships at the autonomous system level and the
nervous system of the worm Caenorhabditis elegans --that have been shaped by
very different dynamics and in very different time-scales--, reveals that
whereas biological evolution has selected a structure close to the optimal
layout, market competition does not necessarily tend toward the most customer
efficient architecture.Comment: 8 pages, 5 figure
Detecting rich-club ordering in complex networks
Uncovering the hidden regularities and organizational principles of networks
arising in physical systems ranging from the molecular level to the scale of
large communication infrastructures is the key issue for the understanding of
their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon
refers to the tendency of nodes with high centrality, the dominant elements of
the system, to form tightly interconnected communities and it is one of the
crucial properties accounting for the formation of dominant communities in both
computer and social sciences [4-8]. Here we provide the analytical expression
and the correct null models which allow for a quantitative discussion of the
rich-club phenomenon. The presented analysis enables the measurement of the
rich-club ordering and its relation with the function and dynamics of networks
in examples drawn from the biological, social and technological domains.Comment: 1 table, 3 figure
Correlation between clustering and degree in affiliation networks
We are interested in the probability that two randomly selected neighbors of
a random vertex of degree (at least) are adjacent. We evaluate this
probability for a power law random intersection graph, where each vertex is
prescribed a collection of attributes and two vertices are adjacent whenever
they share a common attribute. We show that the probability obeys the scaling
as . Our results are mathematically rigorous. The
parameter is determined by the tail indices of power law
random weights defining the links between vertices and attributes
The Blind Watchmaker Network: Scale-freeness and Evolution
It is suggested that the degree distribution for networks of the
cell-metabolism for simple organisms reflects an ubiquitous randomness. This
implies that natural selection has exerted no or very little pressure on the
network degree distribution during evolution. The corresponding random network,
here termed the blind watchmaker network has a power-law degree distribution
with an exponent gamma >= 2. It is random with respect to a complete set of
network states characterized by a description of which links are attached to a
node as well as a time-ordering of these links. No a priory assumption of any
growth mechanism or evolution process is made. It is found that the degree
distribution of the blind watchmaker network agrees very precisely with that of
the metabolic networks. This implies that the evolutionary pathway of the
cell-metabolism, when projected onto a metabolic network representation, has
remained statistically random with respect to a complete set of network states.
This suggests that even a biological system, which due to natural selection has
developed an enormous specificity like the cellular metabolism, nevertheless
can, at the same time, display well defined characteristics emanating from the
ubiquitous inherent random element of Darwinian evolution. The fact that also
completely random networks may have scale-free node distributions gives a new
perspective on the origin of scale-free networks in general.Comment: 5 pages, 3 figure
Consensus clustering in complex networks
The community structure of complex networks reveals both their organization
and hidden relationships among their constituents. Most community detection
methods currently available are not deterministic, and their results typically
depend on the specific random seeds, initial conditions and tie-break rules
adopted for their execution. Consensus clustering is used in data analysis to
generate stable results out of a set of partitions delivered by stochastic
methods. Here we show that consensus clustering can be combined with any
existing method in a self-consistent way, enhancing considerably both the
stability and the accuracy of the resulting partitions. This framework is also
particularly suitable to monitor the evolution of community structure in
temporal networks. An application of consensus clustering to a large citation
network of physics papers demonstrates its capability to keep track of the
birth, death and diversification of topics.Comment: 11 pages, 12 figures. Published in Scientific Report
Popularity versus Similarity in Growing Networks
Popularity is attractive -- this is the formula underlying preferential
attachment, a popular explanation for the emergence of scaling in growing
networks. If new connections are made preferentially to more popular nodes,
then the resulting distribution of the number of connections that nodes have
follows power laws observed in many real networks. Preferential attachment has
been directly validated for some real networks, including the Internet.
Preferential attachment can also be a consequence of different underlying
processes based on node fitness, ranking, optimization, random walks, or
duplication. Here we show that popularity is just one dimension of
attractiveness. Another dimension is similarity. We develop a framework where
new connections, instead of preferring popular nodes, optimize certain
trade-offs between popularity and similarity. The framework admits a geometric
interpretation, in which popularity preference emerges from local optimization.
As opposed to preferential attachment, the optimization framework accurately
describes large-scale evolution of technological (Internet), social (web of
trust), and biological (E.coli metabolic) networks, predicting the probability
of new links in them with a remarkable precision. The developed framework can
thus be used for predicting new links in evolving networks, and provides a
different perspective on preferential attachment as an emergent phenomenon
Emergence of scale-free close-knit friendship structure in online social networks
Despite the structural properties of online social networks have attracted
much attention, the properties of the close-knit friendship structures remain
an important question. Here, we mainly focus on how these mesoscale structures
are affected by the local and global structural properties. Analyzing the data
of four large-scale online social networks reveals several common structural
properties. It is found that not only the local structures given by the
indegree, outdegree, and reciprocal degree distributions follow a similar
scaling behavior, the mesoscale structures represented by the distributions of
close-knit friendship structures also exhibit a similar scaling law. The degree
correlation is very weak over a wide range of the degrees. We propose a simple
directed network model that captures the observed properties. The model
incorporates two mechanisms: reciprocation and preferential attachment. Through
rate equation analysis of our model, the local-scale and mesoscale structural
properties are derived. In the local-scale, the same scaling behavior of
indegree and outdegree distributions stems from indegree and outdegree of nodes
both growing as the same function of the introduction time, and the reciprocal
degree distribution also shows the same power-law due to the linear
relationship between the reciprocal degree and in/outdegree of nodes. In the
mesoscale, the distributions of four closed triples representing close-knit
friendship structures are found to exhibit identical power-laws, a behavior
attributed to the negligible degree correlations. Intriguingly, all the
power-law exponents of the distributions in the local-scale and mesoscale
depend only on one global parameter -- the mean in/outdegree, while both the
mean in/outdegree and the reciprocity together determine the ratio of the
reciprocal degree of a node to its in/outdegree.Comment: 48 pages, 34 figure
Geographic constraints on social network groups
Social groups are fundamental building blocks of human societies. While our
social interactions have always been constrained by geography, it has been
impossible, due to practical difficulties, to evaluate the nature of this
restriction on social group structure. We construct a social network of
individuals whose most frequent geographical locations are also known. We also
classify the individuals into groups according to a community detection
algorithm. We study the variation of geographical span for social groups of
varying sizes, and explore the relationship between topological positions and
geographic positions of their members. We find that small social groups are
geographically very tight, but become much more clumped when the group size
exceeds about 30 members. Also, we find no correlation between the topological
positions and geographic positions of individuals within network communities.
These results suggest that spreading processes face distinct structural and
spatial constraints.Comment: 10 pages, 5 figure
Self-similarity of complex networks
Complex networks have been studied extensively due to their relevance to many
real systems as diverse as the World-Wide-Web (WWW), the Internet, energy
landscapes, biological and social networks
\cite{ab-review,mendes,vespignani,newman,amaral}. A large number of real
networks are called ``scale-free'' because they show a power-law distribution
of the number of links per node \cite{ab-review,barabasi1999,faloutsos}.
However, it is widely believed that complex networks are not {\it length-scale}
invariant or self-similar. This conclusion originates from the ``small-world''
property of these networks, which implies that the number of nodes increases
exponentially with the ``diameter'' of the network
\cite{erdos,bollobas,milgram,watts}, rather than the power-law relation
expected for a self-similar structure. Nevertheless, here we present a novel
approach to the analysis of such networks, revealing that their structure is
indeed self-similar. This result is achieved by the application of a
renormalization procedure which coarse-grains the system into boxes containing
nodes within a given "size". Concurrently, we identify a power-law relation
between the number of boxes needed to cover the network and the size of the box
defining a finite self-similar exponent. These fundamental properties, which
are shown for the WWW, social, cellular and protein-protein interaction
networks, help to understand the emergence of the scale-free property in
complex networks. They suggest a common self-organization dynamics of diverse
networks at different scales into a critical state and in turn bring together
previously unrelated fields: the statistical physics of complex networks with
renormalization group, fractals and critical phenomena.Comment: 28 pages, 12 figures, more informations at http://www.jamlab.or
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