92 research outputs found
Dynamic Computation of Network Statistics via Updating Schema
In this paper we derive an updating scheme for calculating some important
network statistics such as degree, clustering coefficient, etc., aiming at
reduce the amount of computation needed to track the evolving behavior of large
networks; and more importantly, to provide efficient methods for potential use
of modeling the evolution of networks. Using the updating scheme, the network
statistics can be computed and updated easily and much faster than
re-calculating each time for large evolving networks. The update formula can
also be used to determine which edge/node will lead to the extremal change of
network statistics, providing a way of predicting or designing evolution rule
of networks.Comment: 17 pages, 6 figure
Communities and bottlenecks: Trees and treelike networks have high modularity
Much effort has gone into understanding the modular nature of complex
networks. Communities, also known as clusters or modules, are typically
considered to be densely interconnected groups of nodes that are only sparsely
connected to other groups in the network. Discovering high quality communities
is a difficult and important problem in a number of areas. The most popular
approach is the objective function known as modularity, used both to discover
communities and to measure their strength. To understand the modular structure
of networks it is then crucial to know how such functions evaluate different
topologies, what features they account for, and what implicit assumptions they
may make. We show that trees and treelike networks can have unexpectedly and
often arbitrarily high values of modularity. This is surprising since trees are
maximally sparse connected graphs and are not typically considered to possess
modular structure, yet the nonlocal null model used by modularity assigns low
probabilities, and thus high significance, to the densities of these sparse
tree communities. We further study the practical performance of popular methods
on model trees and on a genealogical data set and find that the discovered
communities also have very high modularity, often approaching its maximum
value. Statistical tests reveal the communities in trees to be significant, in
contrast with known results for partitions of sparse, random graphs.Comment: 9 pages, 5 figure
Mesoscopic structure and social aspects of human mobility
The individual movements of large numbers of people are important in many
contexts, from urban planning to disease spreading. Datasets that capture human
mobility are now available and many interesting features have been discovered,
including the ultra-slow spatial growth of individual mobility. However, the
detailed substructures and spatiotemporal flows of mobility - the sets and
sequences of visited locations - have not been well studied. We show that
individual mobility is dominated by small groups of frequently visited,
dynamically close locations, forming primary "habitats" capturing typical daily
activity, along with subsidiary habitats representing additional travel. These
habitats do not correspond to typical contexts such as home or work. The
temporal evolution of mobility within habitats, which constitutes most motion,
is universal across habitats and exhibits scaling patterns both distinct from
all previous observations and unpredicted by current models. The delay to enter
subsidiary habitats is a primary factor in the spatiotemporal growth of human
travel. Interestingly, habitats correlate with non-mobility dynamics such as
communication activity, implying that habitats may influence processes such as
information spreading and revealing new connections between human mobility and
social networks.Comment: 7 pages, 5 figures (main text); 11 pages, 9 figures, 1 table
(supporting information
Portraits of Complex Networks
We propose a method for characterizing large complex networks by introducing
a new matrix structure, unique for a given network, which encodes structural
information; provides useful visualization, even for very large networks; and
allows for rigorous statistical comparison between networks. Dynamic processes
such as percolation can be visualized using animations. Applications to graph
theory are discussed, as are generalizations to weighted networks, real-world
network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure
Evaluating Local Community Methods in Networks
We present a new benchmarking procedure that is unambiguous and specific to
local community-finding methods, allowing one to compare the accuracy of
various methods. We apply this to new and existing algorithms. A simple class
of synthetic benchmark networks is also developed, capable of testing
properties specific to these local methods.Comment: 8 pages, 9 figures, code included with sourc
Modularity measure of networks with overlapping communities
In this paper we introduce a non-fuzzy measure which has been designed to
rank the partitions of a network's nodes into overlapping communities. Such a
measure can be useful for both quantifying clusters detected by various methods
and during finding the overlapping community-structure by optimization methods.
The theoretical problem referring to the separation of overlapping modules is
discussed, and an example for possible applications is given as well
Communities as Well Separated Subgraphs With Cohesive Cores: Identification of Core-Periphery Structures in Link Communities
Communities in networks are commonly considered as highly cohesive subgraphs
which are well separated from the rest of the network. However, cohesion and
separation often cannot be maximized at the same time, which is why a
compromise is sought by some methods. When a compromise is not suitable for the
problem to be solved it might be advantageous to separate the two criteria. In
this paper, we explore such an approach by defining communities as well
separated subgraphs which can have one or more cohesive cores surrounded by
peripheries. We apply this idea to link communities and present an algorithm
for constructing hierarchical core-periphery structures in link communities and
first test results.Comment: 12 pages, 2 figures, submitted version of a paper accepted for the
7th International Conference on Complex Networks and Their Applications,
December 11-13, 2018, Cambridge, UK; revised version at
http://141.20.126.227/~qm/papers
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