263 research outputs found
Searching for network modules
When analyzing complex networks a key target is to uncover their modular
structure, which means searching for a family of modules, namely node subsets
spanning each a subnetwork more densely connected than the average. This work
proposes a novel type of objective function for graph clustering, in the form
of a multilinear polynomial whose coefficients are determined by network
topology. It may be thought of as a potential function, to be maximized, taking
its values on fuzzy clusterings or families of fuzzy subsets of nodes over
which every node distributes a unit membership. When suitably parametrized,
this potential is shown to attain its maximum when every node concentrates its
all unit membership on some module. The output thus is a partition, while the
original discrete optimization problem is turned into a continuous version
allowing to conceive alternative search strategies. The instance of the problem
being a pseudo-Boolean function assigning real-valued cluster scores to node
subsets, modularity maximization is employed to exemplify a so-called quadratic
form, in that the scores of singletons and pairs also fully determine the
scores of larger clusters, while the resulting multilinear polynomial potential
function has degree 2. After considering further quadratic instances, different
from modularity and obtained by interpreting network topology in alternative
manners, a greedy local-search strategy for the continuous framework is
analytically compared with an existing greedy agglomerative procedure for the
discrete case. Overlapping is finally discussed in terms of multiple runs, i.e.
several local searches with different initializations.Comment: 10 page
Detecting hierarchical and overlapping network communities using locally optimal modularity changes
Agglomerative clustering is a well established strategy for identifying
communities in networks. Communities are successively merged into larger
communities, coarsening a network of actors into a more manageable network of
communities. The order in which merges should occur is not in general clear,
necessitating heuristics for selecting pairs of communities to merge. We
describe a hierarchical clustering algorithm based on a local optimality
property. For each edge in the network, we associate the modularity change for
merging the communities it links. For each community vertex, we call the
preferred edge that edge for which the modularity change is maximal. When an
edge is preferred by both vertices that it links, it appears to be the optimal
choice from the local viewpoint. We use the locally optimal edges to define the
algorithm: simultaneously merge all pairs of communities that are connected by
locally optimal edges that would increase the modularity, redetermining the
locally optimal edges after each step and continuing so long as the modularity
can be further increased. We apply the algorithm to model and empirical
networks, demonstrating that it can efficiently produce high-quality community
solutions. We relate the performance and implementation details to the
structure of the resulting community hierarchies. We additionally consider a
complementary local clustering algorithm, describing how to identify
overlapping communities based on the local optimality condition.Comment: 10 pages; 4 tables, 3 figure
Efficient modularity density heuristics in graph clustering and their applications
Modularity Density Maximization is a graph clustering problem which avoids the resolution limit degeneracy of the Modularity Maximization problem. This thesis aims at solving larger instances than current Modularity Density heuristics do, and show how close the obtained solutions are to the expected clustering. Three main contributions arise from this objective. The first one is about the theoretical contributions about properties of Modularity Density based prioritizers. The second one is the development of eight Modularity Density Maximization heuristics. Our heuristics are compared with optimal results from the literature, and with GAOD, iMeme-Net, HAIN, BMD- heuristics. Our results are also compared with CNM and Louvain which are heuristics for Modularity Maximization that solve instances with thousands of nodes. The tests were carried out by using graphs from the “Stanford Large Network Dataset Collection”. The experiments have shown that our eight heuristics found solutions for graphs with hundreds of thousands of nodes. Our results have also shown that five of our heuristics surpassed the current state-of-the-art Modularity Density Maximization heuristic solvers for large graphs. A third contribution is the proposal of six column generation methods. These methods use exact and heuristic auxiliary solvers and an initial variable generator. Comparisons among our proposed column generations and state-of-the-art algorithms were also carried out. The results showed that: (i) two of our methods surpassed the state-of-the-art algorithms in terms of time, and (ii) our methods proved the optimal value for larger instances than current approaches can tackle. Our results suggest clear improvements to the state-of-the-art results for the Modularity Density Maximization problem
Fast Detection of Community Structures using Graph Traversal in Social Networks
Finding community structures in social networks is considered to be a
challenging task as many of the proposed algorithms are computationally
expensive and does not scale well for large graphs. Most of the community
detection algorithms proposed till date are unsuitable for applications that
would require detection of communities in real-time, especially for massive
networks. The Louvain method, which uses modularity maximization to detect
clusters, is usually considered to be one of the fastest community detection
algorithms even without any provable bound on its running time. We propose a
novel graph traversal-based community detection framework, which not only runs
faster than the Louvain method but also generates clusters of better quality
for most of the benchmark datasets. We show that our algorithms run in O(|V | +
|E|) time to create an initial cover before using modularity maximization to
get the final cover.
Keywords - community detection; Influenced Neighbor Score; brokers; community
nodes; communitiesComment: 29 pages, 9 tables, and 13 figures. Accepted in "Knowledge and
Information Systems", 201
Identifying the community structure of the international food-trade multi network
Achieving international food security requires improved understanding of how
international trade networks connect countries around the world through the
import-export flows of food commodities. The properties of food trade networks
are still poorly documented, especially from a multi-network perspective. In
particular, nothing is known about the community structure of food networks,
which is key to understanding how major disruptions or 'shocks' would impact
the global food system. Here we find that the individual layers of this network
have densely connected trading groups, a consistent characteristic over the
period 2001 to 2011. We also fit econometric models to identify social,
economic and geographic factors explaining the probability that any two
countries are co-present in the same community. Our estimates indicate that the
probability of country pairs belonging to the same food trade community depends
more on geopolitical and economic factors -- such as geographical proximity and
trade agreements co-membership -- than on country economic size and/or income.
This is in sharp contrast with what we know about bilateral-trade determinants
and suggests that food country communities behave in ways that can be very
different from their non-food counterparts.Comment: 47 pages, 19 figure
A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme
The study of network structure is pervasive in sociology, biology, computer
science, and many other disciplines. One of the most important areas of network
science is the algorithmic detection of cohesive groups of nodes called
"communities". One popular approach to find communities is to maximize a
quality function known as {\em modularity} to achieve some sort of optimal
clustering of nodes. In this paper, we interpret the modularity function from a
novel perspective: we reformulate modularity optimization as a minimization
problem of an energy functional that consists of a total variation term and an
balance term. By employing numerical techniques from image processing
and compressive sensing -- such as convex splitting and the
Merriman-Bence-Osher (MBO) scheme -- we develop a variational algorithm for the
minimization problem. We present our computational results using both synthetic
benchmark networks and real data.Comment: 23 page
Generating realistic scaled complex networks
Research on generative models is a central project in the emerging field of
network science, and it studies how statistical patterns found in real networks
could be generated by formal rules. Output from these generative models is then
the basis for designing and evaluating computational methods on networks, and
for verification and simulation studies. During the last two decades, a variety
of models has been proposed with an ultimate goal of achieving comprehensive
realism for the generated networks. In this study, we (a) introduce a new
generator, termed ReCoN; (b) explore how ReCoN and some existing models can be
fitted to an original network to produce a structurally similar replica, (c)
use ReCoN to produce networks much larger than the original exemplar, and
finally (d) discuss open problems and promising research directions. In a
comparative experimental study, we find that ReCoN is often superior to many
other state-of-the-art network generation methods. We argue that ReCoN is a
scalable and effective tool for modeling a given network while preserving
important properties at both micro- and macroscopic scales, and for scaling the
exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the
paper was presented at the 5th International Workshop on Complex Networks and
their Application
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