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• 1
Article
Language: English
In: Physical review. E, Statistical, nonlinear, and soft matter physics, July 2011, Vol.84(1 Pt 2), pp.016104
Description: We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure and (ii) when local dynamics is described by the same evolution equation, the model is decomposable, with the equilibrium behavior of the system expressed as an explicit function of network topology and node dynamics.
Keywords: Models, Theoretical
E-ISSN: 1550-2376
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• 2
Article
Language: English
In: Physical review. E, Statistical, nonlinear, and soft matter physics, January 2012, Vol.85(1 Pt 2), pp.016114
Description: The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network, such as the largest eigenvalue of a topology related matrix. However, little is known about the direct influence of the network topology on the microscopic level, such as the influence of the (neighboring) network on the probability of a particular node's infection. To answer this question, we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible-infective-susceptible model for two cases of spreading processes: reactive and contact processes. The bounds are derived by considering the n-hop neighborhood of the node; the bounds are tighter as one uses a larger n-hop neighborhood to calculate them. Consequently, using local information for different neighborhood sizes, we assess the extent to which the topology influences the spreading process, thus providing also a strong macroscopic connection between the former and the latter. Our findings are complemented by numerical results for a real-world email network. A very good estimate for the infection density ρ is obtained using only two-hop neighborhoods, which account for 0.4% of the entire network topology on average.
Keywords: Models, Theoretical ; Communicable Diseases -- Epidemiology
E-ISSN: 1550-2376
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• 3
Article
Language: English
In: Physical review. E, Statistical, nonlinear, and soft matter physics, October 2011, Vol.84(4 Pt 2), pp.046102
Description: Communities are not static; they evolve, split and merge, appear and disappear, i.e., they are the product of dynamical processes that govern the evolution of a network. A good algorithm for community detection should not only quantify the topology of the network but incorporate the dynamical processes that take place on the network. We present an algorithm for community detection that combines network structure with processes that support the creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes the node's involvement in each community. This way, in addition to the overlapping communities, we can identify nodes that are good followers of their leader and also nodes with no clear community involvement that serve as proxies between several communities and that are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results, including other possible applications.
Keywords: Physics - Physics And Society ; Condensed Matter - Statistical Mechanics ; Computer Science - Social And Information Networks;
E-ISSN: 1550-2376
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• 4
Article
Language: English
In: Physica A: Statistical Mechanics and its Applications, 2010, Vol.389(11), pp.2290-2299
Description: Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that “elite” papers are cited by other “elite” papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that “elite” patents are cited by other “elite” patents. Finally, for email communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.
Keywords: Directed Networks ; Rich-Club Coefficient ; Page-Club Coefficient ; Real Networks ; Physics
ISSN: 0378-4371
E-ISSN: 1873-2119
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• 5
Article
In: Scientific Reports, 2014, Vol.4
Description: The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that-for the SIS model-differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node's degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals.
Keywords: Nodes ; Spreading ; Epidemics ; Epidemics;
ISSN: 20452322
E-ISSN: 20452322
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• 6
Article
Description: The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network, such as the largest eigenvalue of a topology related matrix. However, little is known about the direct influence of the network topology on microscopic level, such as the influence of the (neighboring) network on the probability of a particular node's infection. To answer this question, we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible-infective-susceptible model for two cases of spreading processes: reactive and contact processes. The bounds are derived by considering the $n-$hop neighborhood of the node; the bounds are tighter as one uses a larger $n-$hop neighborhood to calculate them. Consequently, using local information for different neighborhood sizes, we assess the extent to which the topology influences the spreading process, thus providing also a strong macroscopic connection between the former and the latter. Our findings are complemented by numerical results for a real-world e-mail network. A very good estimate for the infection density $\rho$ is obtained using only 2-hop neighborhoods which account for 0.4% of the entire network topology on average. Comment: 11 pages, 6 figures
Keywords: Physics - Physics And Society ; Condensed Matter - Statistical Mechanics ; Computer Science - Social And Information Networks
Source: Cornell University
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• 7
Article
Description: The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that--for the SIS model--differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node's degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals. Comment: 13 pages, 2 figures
Keywords: Physics - Physics And Society ; Computer Science - Social And Information Networks ; Quantitative Biology - Populations And Evolution
Source: Cornell University
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• 8
Article
Language: English
In: Physica A: Statistical Mechanics and its Applications, 2010, Vol.389(23), pp.5538-5549
Description: We propose a metric for vulnerability of labeled graphs that has the following two properties: (1) when the labeled graph is considered as an unlabeled one, the metric reduces to the corresponding metric for an unlabeled graph; and (2) the metric has the same value for differently labeled fully connected graphs, reflecting the notion that any arbitrarily labeled fully connected topology is equally vulnerable as any other. A vulnerability analysis of two real-world networks, the power grid of the European Union, and an autonomous system network, has been performed. The networks have been treated as graphs with node labels. The analysis consists of calculating characteristic path lengths between labels of nodes and determining largest connected cluster size under two node and edge attack strategies. Results obtained are more informative of the networks’ vulnerability compared to the case when the networks are modeled with unlabeled graphs.
Keywords: Labeled Networks ; Vulnerability ; Eu Power Grid ; As Network ; Physics
ISSN: 0378-4371
E-ISSN: 1873-2119
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