3,844 research outputs found
Network 'small-world-ness': a quantitative method for determining canonical network equivalence
Background: Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model-the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified.
Methodology/Principal Findings: We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S. 1-an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process.
Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing
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
Colored Motifs Reveal Computational Building Blocks in the C. elegans Brain
Background: Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional
organization of the network as a whole. However, these structural
motifs can only tell one part of the functional story because in this
analysis each node and edge is treated on an equal footing. In real
networks, two motifs that are topologically identical but whose nodes
perform very different functions will play very different roles in the
network.
Methodology/Principal Findings: Here, we combine structural information
derived from the topology of the neuronal network of the nematode C.
elegans with information about the biological function of these nodes,
thus coloring nodes by function. We discover that particular
colorations of motifs are significantly more abundant in the worm brain
than expected by chance, and have particular computational functions
that emphasize the feed-forward structure of information processing in
the network, while evading feedback loops. Interneurons are strongly
over-represented among the common motifs, supporting the notion that
these motifs process and transduce the information from the sensor
neurons towards the muscles. Some of the most common motifs identified
in the search for significant colored motifs play a crucial role in the
system of neurons controlling the worm's locomotion.
Conclusions/Significance: The analysis of complex networks in terms of
colored motifs combines two independent data sets to generate insight
about these networks that cannot be obtained with either data set
alone. The method is general and should allow a decomposition of any
complex networks into its functional (rather than topological) motifs
as long as both wiring and functional information is available
Spectral plots and the representation and interpretation of biological data
It is basic question in biology and other fields to identify the char-
acteristic properties that on one hand are shared by structures from a
particular realm, like gene regulation, protein-protein interaction or neu- ral
networks or foodwebs, and that on the other hand distinguish them from other
structures. We introduce and apply a general method, based on the spectrum of
the normalized graph Laplacian, that yields repre- sentations, the spectral
plots, that allow us to find and visualize such properties systematically. We
present such visualizations for a wide range of biological networks and compare
them with those for networks derived from theoretical schemes. The differences
that we find are quite striking and suggest that the search for universal
properties of biological networks should be complemented by an understanding of
more specific features of biological organization principles at different
scales.Comment: 15 pages, 7 figure
Mental health and the impact of ubiquitous technologies
This Theme issue focuses on the emerging research of ubiquitous technologies to support mental health. So far, the majority of work presented in the field of ubiquitous healthcare has focused on supporting people affected by somatic diseases. However, increasing number of diseases affecting mental health has prompted research on technologies to support people suffering from these diseases. This Theme issue provides a number of examples of research on the potential impact of ubiquitous technologies in the field of mental health
Mesoscopic organization reveals the constraints governing C. elegans nervous system
One of the biggest challenges in biology is to understand how activity at the
cellular level of neurons, as a result of their mutual interactions, leads to
the observed behavior of an organism responding to a variety of environmental
stimuli. Investigating the intermediate or mesoscopic level of organization in
the nervous system is a vital step towards understanding how the integration of
micro-level dynamics results in macro-level functioning. In this paper, we have
considered the somatic nervous system of the nematode Caenorhabditis elegans,
for which the entire neuronal connectivity diagram is known. We focus on the
organization of the system into modules, i.e., neuronal groups having
relatively higher connection density compared to that of the overall network.
We show that this mesoscopic feature cannot be explained exclusively in terms
of considerations, such as optimizing for resource constraints (viz., total
wiring cost) and communication efficiency (i.e., network path length).
Comparison with other complex networks designed for efficient transport (of
signals or resources) implies that neuronal networks form a distinct class.
This suggests that the principal function of the network, viz., processing of
sensory information resulting in appropriate motor response, may be playing a
vital role in determining the connection topology. Using modular spectral
analysis, we make explicit the intimate relation between function and structure
in the nervous system. This is further brought out by identifying functionally
critical neurons purely on the basis of patterns of intra- and inter-modular
connections. Our study reveals how the design of the nervous system reflects
several constraints, including its key functional role as a processor of
information.Comment: Published version, Minor modifications, 16 pages, 9 figure
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
Effect of correlations on network controllability
A dynamical system is controllable if by imposing appropriate external
signals on a subset of its nodes, it can be driven from any initial state to
any desired state in finite time. Here we study the impact of various network
characteristics on the minimal number of driver nodes required to control a
network. We find that clustering and modularity have no discernible impact, but
the symmetries of the underlying matching problem can produce linear, quadratic
or no dependence on degree correlation coefficients, depending on the nature of
the underlying correlations. The results are supported by numerical simulations
and help narrow the observed gap between the predicted and the observed number
of driver nodes in real networks
Correlated dynamics in egocentric communication networks
We investigate the communication sequences of millions of people through two
different channels and analyze the fine grained temporal structure of
correlated event trains induced by single individuals. By focusing on
correlations between the heterogeneous dynamics and the topology of egocentric
networks we find that the bursty trains usually evolve for pairs of individuals
rather than for the ego and his/her several neighbors thus burstiness is a
property of the links rather than of the nodes. We compare the directional
balance of calls and short messages within bursty trains to the average on the
actual link and show that for the trains of voice calls the imbalance is
significantly enhanced, while for short messages the balance within the trains
increases. These effects can be partly traced back to the technological
constrains (for short messages) and partly to the human behavioral features
(voice calls). We define a model that is able to reproduce the empirical
results and may help us to understand better the mechanisms driving technology
mediated human communication dynamics.Comment: 7 pages, 6 figure
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