54,023 research outputs found
Stability of graph communities across time scales
The complexity of biological, social and engineering networks makes it
desirable to find natural partitions into communities that can act as
simplified descriptions and provide insight into the structure and function of
the overall system. Although community detection methods abound, there is a
lack of consensus on how to quantify and rank the quality of partitions. We
show here that the quality of a partition can be measured in terms of its
stability, defined in terms of the clustered autocovariance of a Markov process
taking place on the graph. Because the stability has an intrinsic dependence on
time scales of the graph, it allows us to compare and rank partitions at each
time and also to establish the time spans over which partitions are optimal.
Hence the Markov time acts effectively as an intrinsic resolution parameter
that establishes a hierarchy of increasingly coarser clusterings. Within our
framework we can then provide a unifying view of several standard partitioning
measures: modularity and normalized cut size can be interpreted as one-step
time measures, whereas Fiedler's spectral clustering emerges at long times. We
apply our method to characterize the relevance and persistence of partitions
over time for constructive and real networks, including hierarchical graphs and
social networks. We also obtain reduced descriptions for atomic level protein
structures over different time scales.Comment: submitted; updated bibliography from v
Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction
Despite the recognized importance of the multi-scale spatio-temporal
organization of proteins, most computational tools can only access a limited
spectrum of time and spatial scales, thereby ignoring the effects on protein
behavior of the intricate coupling between the different scales. Starting from
a physico-chemical atomistic network of interactions that encodes the structure
of the protein, we introduce a methodology based on multi-scale graph
partitioning that can uncover partitions and levels of organization of proteins
that span the whole range of scales, revealing biological features occurring at
different levels of organization and tracking their effect across scales.
Additionally, we introduce a measure of robustness to quantify the relevance of
the partitions through the generation of biochemically-motivated surrogate
random graph models. We apply the method to four distinct conformations of
myosin tail interacting protein, a protein from the molecular motor of the
malaria parasite, and study properties that have been experimentally addressed
such as the closing mechanism, the presence of conserved clusters, and the
identification through computational mutational analysis of key residues for
binding.Comment: 13 pages, 7 Postscript figure
The stability of a graph partition: A dynamics-based framework for community detection
Recent years have seen a surge of interest in the analysis of complex
networks, facilitated by the availability of relational data and the
increasingly powerful computational resources that can be employed for their
analysis. Naturally, the study of real-world systems leads to highly complex
networks and a current challenge is to extract intelligible, simplified
descriptions from the network in terms of relevant subgraphs, which can provide
insight into the structure and function of the overall system.
Sparked by seminal work by Newman and Girvan, an interesting line of research
has been devoted to investigating modular community structure in networks,
revitalising the classic problem of graph partitioning.
However, modular or community structure in networks has notoriously evaded
rigorous definition. The most accepted notion of community is perhaps that of a
group of elements which exhibit a stronger level of interaction within
themselves than with the elements outside the community. This concept has
resulted in a plethora of computational methods and heuristics for community
detection. Nevertheless a firm theoretical understanding of most of these
methods, in terms of how they operate and what they are supposed to detect, is
still lacking to date.
Here, we will develop a dynamical perspective towards community detection
enabling us to define a measure named the stability of a graph partition. It
will be shown that a number of previously ad-hoc defined heuristics for
community detection can be seen as particular cases of our method providing us
with a dynamic reinterpretation of those measures. Our dynamics-based approach
thus serves as a unifying framework to gain a deeper understanding of different
aspects and problems associated with community detection and allows us to
propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte
Community detection and role identification in directed networks: understanding the Twitter network of the care.data debate
With the rise of social media as an important channel for the debate and discussion of public affairs, online social networks such as Twitter have become important platforms for public information and engagement by policy makers. To communicate effectively through Twitter, policy makers need to understand how influence and interest propagate within its network of users. In this chapter we use graph-theoretic methods to analyse the Twitter debate surrounding NHS Englands controversial care.data scheme. Directionality is a crucial feature of the Twitter social graph - information flows from the followed to the followers - but is often ignored in social network analyses; our methods are based on the behaviour of dynamic processes on the network and can be applied naturally to directed networks. We uncover robust communities of users and show that these communities reflect how information flows through the Twitter network. We are also able to classify users by their differing roles in directing the flow of information through the network. Our methods and results will be useful to policy makers who would like to use Twitter effectively as a communication medium
Interest communities and flow roles in directed networks: the Twitter network of the UK riots
Directionality is a crucial ingredient in many complex networks in which
information, energy or influence are transmitted. In such directed networks,
analysing flows (and not only the strength of connections) is crucial to reveal
important features of the network that might go undetected if the orientation
of connections is ignored. We showcase here a flow-based approach for community
detection in networks through the study of the network of the most influential
Twitter users during the 2011 riots in England. Firstly, we use directed Markov
Stability to extract descriptions of the network at different levels of
coarseness in terms of interest communities, i.e., groups of nodes within which
flows of information are contained and reinforced. Such interest communities
reveal user groupings according to location, profession, employer, and topic.
The study of flows also allows us to generate an interest distance, which
affords a personalised view of the attention in the network as viewed from the
vantage point of any given user. Secondly, we analyse the profiles of incoming
and outgoing long-range flows with a combined approach of role-based similarity
and the novel relaxed minimum spanning tree algorithm to reveal that the users
in the network can be classified into five roles. These flow roles go beyond
the standard leader/follower dichotomy and differ from classifications based on
regular/structural equivalence. We then show that the interest communities fall
into distinct informational organigrams characterised by a different mix of
user roles reflecting the quality of dialogue within them. Our generic
framework can be used to provide insight into how flows are generated,
distributed, preserved and consumed in directed networks.Comment: 32 pages, 14 figures. Supplementary Spreadsheet available from:
http://www2.imperial.ac.uk/~mbegueri/Docs/riotsCommunities.zip or
http://rsif.royalsocietypublishing.org/content/11/101/20140940/suppl/DC
Finding role communities in directed networks using Role-Based Similarity, Markov Stability and the Relaxed Minimum Spanning Tree
We present a framework to cluster nodes in directed networks according to
their roles by combining Role-Based Similarity (RBS) and Markov Stability, two
techniques based on flows. First we compute the RBS matrix, which contains the
pairwise similarities between nodes according to the scaled number of in- and
out-directed paths of different lengths. The weighted RBS similarity matrix is
then transformed into an undirected similarity network using the Relaxed
Minimum-Spanning Tree (RMST) algorithm, which uses the geometric structure of
the RBS matrix to unblur the network, such that edges between nodes with high,
direct RBS are preserved. Finally, we partition the RMST similarity network
into role-communities of nodes at all scales using Markov Stability to find a
robust set of roles in the network. We showcase our framework through a
biological and a man-made network.Comment: 4 pages, 2 figure
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