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Graph theory and networks in biology
 IET Systems Biology, 1:89 – 119
, 2007
"... In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarch ..."
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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1
Analysing Information Flows and Key Mediators through Temporal Centrality Metrics
"... The study of influential members of human networks is an important research question in social network analysis. However, the current stateoftheart is based on static or aggregated representation of the network topology. We argue that dynamically evolving network topologies are inherent in many s ..."
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Cited by 34 (5 self)
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The study of influential members of human networks is an important research question in social network analysis. However, the current stateoftheart is based on static or aggregated representation of the network topology. We argue that dynamically evolving network topologies are inherent in many systems, including real online social and technological networks: fortunately the nature of these systems is such that they allow the gathering of large quantities of finegrained temporal data on interactions amongst the network members. In this paper we propose novel temporal centrality metrics which take into account such dynamic interactions over time. Using a real corporate email dataset we evaluate the important individuals selected by means of static and temporal analysis taking two perspectives: firstly, from a semantic level, we investigate their corporate role in the organisation; and secondly, from a dynamic process point of view, we measure information dissemination and the role of information mediators. We find that temporal analysis provides a better understanding of dynamic processes and a more accurate identification of important people compared to traditional static methods.
HADI: Mining radii of large graphs
 ACM Transactions on Knowledge Discovery from Data
, 2010
"... Given large, multimillion node graphs (e.g., Facebook, webcrawls, etc.), how do they evolve over time? How are they connected? What are the central nodes and the outliers? In this paper we define the Radius plot of a graph and show how it can answer these questions. However, computing the Radius p ..."
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Cited by 33 (10 self)
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Given large, multimillion node graphs (e.g., Facebook, webcrawls, etc.), how do they evolve over time? How are they connected? What are the central nodes and the outliers? In this paper we define the Radius plot of a graph and show how it can answer these questions. However, computing the Radius plot is prohibitively expensive for graphs reaching the planetary scale. There are two major contributions in this paper: (a) We propose HADI (HAdoop DIameter and radii estimator), a carefully designed and finetuned algorithm to compute the radii and the diameter of massive graphs, that runs on the top of the Hadoop/MapReduce system, with excellent scaleup on the number of available machines (b) We run HADI on several real world datasets including YahooWeb (6B edges, 1/8 of a Terabyte), one of the largest public graphs ever analyzed. Thanks to HADI, we report fascinating patterns on large networks, like the surprisingly small effective diameter, the multimodal/bimodal shape of the Radius plot, and its palindrome motion over time.
Centrality Measures Based on Current Flow
, 2005
"... We consider variations of two wellknown centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the currentflow variant of close ..."
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Cited by 32 (2 self)
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We consider variations of two wellknown centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the currentflow variant of closeness centrality is identical with another known measure, information centrality, and give improved algorithms for computing both measures exactly. Since running times and space requirements are prohibitive for large networks, we also present a randomized approximation scheme for currentflow betweenness.
Network Properties Revealed Through Matrix Functions
, 2008
"... The newly emerging field of Network Science deals with the tasks of modelling, comparing and summarizing large data sets that describe complex interactions. Because pairwise affinity data can be stored in a twodimensional array, graph theory and applied linear algebra provide extremely useful tools. ..."
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Cited by 30 (3 self)
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The newly emerging field of Network Science deals with the tasks of modelling, comparing and summarizing large data sets that describe complex interactions. Because pairwise affinity data can be stored in a twodimensional array, graph theory and applied linear algebra provide extremely useful tools. Here, we focus on the general concepts of centrality, communicability and betweenness, each of which quantifies important features in a network. Some recent work in the mathematical physics literature has shown that the exponential of a network’s adjacency matrix can be used as the basis for defining and computing specific versions of these measures. We introduce here a general class of measures based on matrix functions, and show that a particular case involving a matrix resolvent arises naturally from graphtheoretic arguments. We also point out connections between these measures and the quantities typically computed when spectral methods are used for data mining tasks such as clustering and ordering. We finish with computational examples showing the new matrix resolvent version applied to real networks.
Sybil attacks against mobile users: friends and foes to the rescue
 In INFOCOM
, 2010
"... Abstract—Collaborative applications for colocated mobile users can be severely disrupted by a sybil attack to the point of being unusable. Existing decentralized defences have largely been designed for peertopeer networks but not for mobile networks. That is why we propose a new decentralized def ..."
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Abstract—Collaborative applications for colocated mobile users can be severely disrupted by a sybil attack to the point of being unusable. Existing decentralized defences have largely been designed for peertopeer networks but not for mobile networks. That is why we propose a new decentralized defence for portable devices and call it MobID. The idea is that a device manages two small networks in which it stores information about the devices it meets: its network of friends contains honest devices, and its network of foes contains suspicious devices. By reasoning on these two networks, the device is then able to determine whether an unknown individual is carrying out a sybil attack or not. We evaluate the extent to which MobID reduces the number of interactions with sybil attackers and consequently enables collaborative applications. We do so using real mobility and social network data. We also assess computational and communication costs of MobID on mobile phones. I.
A survey of socialbased routing in delay tolerant networks: positive and negative social effects
 Communications Surveys & Tutorials, IEEE 15.1
, 2013
"... Abstract—Delay tolerant networks (DTNs) may lack continuous network connectivity. Routing in DTNs is thus challenging since it must handle network partitioning, long delays, and dynamic topology in such networks. In recent years, socialbased approaches, which attempt to exploit social behaviors of ..."
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Cited by 26 (7 self)
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Abstract—Delay tolerant networks (DTNs) may lack continuous network connectivity. Routing in DTNs is thus challenging since it must handle network partitioning, long delays, and dynamic topology in such networks. In recent years, socialbased approaches, which attempt to exploit social behaviors of DTN nodes to make better routing decision, have drawn tremendous interests in DTN routing design. In this article, we summarize the social properties in DTNs, and provide a survey of recent socialbased DTN routing approaches. To improve routing performance, these methods either take advantages of positive social characteristics such as community and friendship to assist packet forwarding or consider negative social characteristics such as selfishness. We conclude by discussing some open issues and challenges in socialbased approaches regarding the design of DTN routing protocols. Index Terms—DTN routing; Socialbased approaches; Social graphs; Social network analysis; Delay tolerant networks.
On the Vulnerability of Large Graphs
"... Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k node ..."
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Cited by 26 (11 self)
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Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k nodes and (c) a fast algorithm to choose the best such k nodes. We answer all these three questions: we give the justification behind our choices, we show that they agree with intuition as well as recent results in immunology. Moreover, we propose NetShield, a fast and scalable algorithm. Finally, we give experiments on large real graphs, where NetShield achieves tremendous speed savings exceeding 7 orders of magnitude, against straightforward competitors. 1
Comparison of Centralities for Biological Networks
 Proc German Conf Bioinformatics (GCB'04), Volume P53 of LNI
, 2004
"... The analysis of biological networks involves the evaluation of the vertices within the connection structure of the network. To support this analysis we discuss five centrality measures and demonstrate their applicability on two example networks, a proteinproteininteraction network and a transcript ..."
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Cited by 25 (4 self)
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The analysis of biological networks involves the evaluation of the vertices within the connection structure of the network. To support this analysis we discuss five centrality measures and demonstrate their applicability on two example networks, a proteinproteininteraction network and a transcriptional regulation network. We show that all five centrality measures result in different valuations of the vertices and that for the analysis of biological networks all five measures are of interest.
A family of dissimilarity measures between nodes generalizing both the shortestpath and the commutetime distances
 in Proceedings of the 14th SIGKDD International Conference on Knowledge Discovery and Data Mining
"... This work introduces a new family of linkbased dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortestpath (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortestpath d ..."
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Cited by 24 (11 self)
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This work introduces a new family of linkbased dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortestpath (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortestpath distance when θ is large and, on the other end, to the commutetime (or resistance) distance when θ is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy (related to θ) spread in the graph. The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortestpath policy. By adopting a statistical physics approach and computing a sum over all the possible paths (discrete path integral), it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations, where n is the number of nodes. On the other hand, the dissimilarity between every couple of nodes is obtained by inverting an n × n matrix. The proposed measure can be used for various graph mining tasks such as computing betweenness centrality, finding dense communities, etc, as shown in the experimental section.