Showing papers in "Journal of Complex Networks in 2017"

Information cascades in complex networks

Abstract: Information cascades are important dynamical processes in complex networks. An information cascade can describe the spreading dynamics of rumour, disease, memes, or marketing campaigns, which initially start from a node or a set of nodes in the network. If conditions are right, information cascades rapidly encompass large parts of the network, thus leading to epidemics or epidemic spreading. Certain network topologies are particularly conducive to epidemics, while others decelerate and even prohibit rapid information spreading. Here we review models that describe information cascades in complex networks, with an emphasis on the role and consequences of node centrality. In particular, we present simulation results on sample networks that reveal just how relevant the centrality of initiator nodes is on the latter development of an information cascade, and we define the spreading influence of a node as the fraction of nodes that is activated as a result of the initial activation of that node. A systemic review of existing results shows that some centrality measures, such as the degree and betweenness, are positively correlated with the spreading influence, while other centrality measures, such as eccentricity and the information index, have negative correlation. A positive correlation implies that choosing a node with the highest centrality value will activate the largest number of nodes, while a negative correlation implies that the node with the lowest centrality value will have the same effect.We discuss possible applications of these results, and we emphasize how information cascades can help us identify nodes with the highest spreading capability in complex networks.

Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows

Abstract: We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with established node-based characteristics. Our work suggests a number of applications for data mining, including denoising and clustering of experimental data, as well as extrapolation of network evolution.

Generating Bipartite Networks with a Prescribed Joint Degree Distribution.

Abstract: We describe a class of new algorithms to construct bipartite networks that preserves a prescribed degree and joint-degree (degree-degree) distribution of the nodes. Bipartite networks are graphs that can represent real-world interactions between two disjoint sets, such as actor-movie networks, author-article networks, co-occurrence networks, and heterosexual partnership networks. Often there is a strong correlation between the degree of a node and the degrees of the neighbors of that node that must be preserved when generating a network that reflects the structure of the underling system. Our bipartite 2K (B2K) algorithms generate an ensemble of networks that preserve prescribed degree sequences for the two disjoint set of nodes in the bipartite network, and the joint-degree distribution that is the distribution of the degrees of all neighbors of nodes with the same degree. We illustrate the effectiveness of the algorithms on a romance network using the NetworkX software environment to compare other properties of a target network that are not directly enforced by the B2K algorithms. We observe that when average degree of nodes is low, as is the case for romance and heterosexual partnership networks, then the B2K networks tend to preserve additional properties, such as the cluster coefficients, than algorithms that do not preserve the joint-degree distribution of the original network.

Rentian scaling for the measurement of optimal embedding of complex networks into physical space

Abstract: The London Underground is one of the largest, oldest and most widely used systems of public transit in the world. Transportation in London is constantly challenged to expand and adapt its system to meet the changing requirements of London's populace while maintaining a cost-effective and efficient network. Previous studies have described this system using concepts from graph theory, reporting network diagnostics and core-periphery architecture. These studies provide information about the basic structure and efficiency of this network; however, the question of system optimization in the context of evolving demands is seldom investigated. In this paper we examined the cost effectiveness of the topological-physical embedding of the Tube using estimations of the topological dimension, wiring length and Rentian scaling, an isometric scaling relationship between the number of elements and connections in a system. We measured these properties in both two- and three-dimensional embeddings of the networks into Euclidean space, as well as between two time points, and across the densely interconnected core and sparsely interconnected periphery. While the two- and three-dimensional representations of the present-day Tube exhibit Rentian scaling relationships between nodes and edges of the system, the overall network is approximately cost-efficiently embedded into its physical environment in two dimensions, but not in three. We further investigated a notable disparity in the topology of the network's local core versus its more extended periphery, suggesting an underlying relationship between meso-scale structure and physical embedding. The collective findings from this study, including changes in Rentian scaling over time, provide evidence for differential embedding efficiency in planned versus self-organized networks. These findings suggest that concepts of optimal physical embedding can be applied more broadly to other physical systems whose links are embedded in a well-defined space, and whose topology is constrained by a cost function that minimizes link lengths within that space.

Structural bounds on the dyadic effect

Abstract: In this paper we consider the dyadic effect introduced in complex networks when nodes are distinguished by a binary characteristic. Under these circumstances two independent parameters, namely dyadicity and heterophilicity, are able to measure how much the assigned characteristic affects the network topology. All possible configurations can be represented in a phase diagram lying in a two-dimensional space that represents the feasible region of the dyadic effect, which is bound by two upper bounds on dyadicity and heterophilicity. Using some network structural arguments, we are able to improve such upper bounds and introduce two new lower bounds, providing a reduction of the feasible region of the dyadic effect as well as constraining dyadicity and heterophilicity within a specific range. Some computational experiences show the bounds effectiveness and their usefulness with regards to different classes of networks.

Evaluating balance on social networks from their simple cycles

Abstract: Signed networks have long been used to represent social relations of amity (+) and enmity (-) between individuals. Group of individuals who are cyclically connected are said to be balanced if the number of negative edges in the cycle is even and unbalanced otherwise. In its earliest and most natural formulation, the balance of a social network was thus defined from its simple cycles, cycles which do not visit any vertex more than once. Because of the inherent difficulty associated with finding such cycles on very large networks, social balance has since then been studied via other means. In this article we present the balance as measured from the simple cycles and primitive orbits of social networks. We specifically provide two measures of balance: the proportion R` of negative simple cycles of length ` for each ` 6 20 which generalises the triangle index, and a ratio K` which extends the relative signed clustering coefficient introduced by Kunegis. To do so, we use a Monte Carlo implementation of a novel exact formula for counting the simple cycles on any weighted directed graph. Our method is free from the double-counting problem affecting previous cycle-based approaches, does not require edge-reciprocity of the underlying network, provides a gray-scale measure of balance for each cycle length separately and is sufficiently tractable that it can be implemented on a standard desktop computer. We observe that social networks exhibit strong inter-edge correlations favouring balanced situations and we determine the corresponding correlation length x . For longer simple cycles, R` undergoes a sharp transition to values expected from an uncorrelated model. This transition is absent from synthetic random networks, strongly suggesting that it carries a sociological meaning warranting further research.

Contact process with exogenous infection and the scaled SIS process

Abstract: Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process with nonzero exogenous infection rate (also known as the {\epsilon}-SIS, {\epsilon} susceptible-infected-susceptible, model [1]). The only known analytical characterization of the equilibrium distribution of this process is for complete networks. For large networks with arbitrary topology, it is infeasible to numerically solve for the equilibrium distribution since it requires solving the eigenvalue-eigenvector problem of a matrix that is exponential in N , the size of the network. We show that, for a certain range of the network process parameters, the equilibrium distribution of the extended contact process on arbitrary, finite-size networks is well approximated by the equilibrium distribution of the scaled SIS process, which we derived in closed-form in prior work. We confirm this result with numerical simulations comparing the equilibrium distribution of the extended contact process with that of a scaled SIS process. We use this approximation to decide, in polynomial-time, which agents and network substructures are more susceptible to infection by the extended contact process.

Network partition via a bound of the spectral radius

Abstract: Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this set as the spectral– core. The degree of the nodes of the subnetwork formed by the spectral–core gives an approximation to the top entries of the leading eigenvector of the whole network. We also present some numerical examples showing the dependancy of the spectral–core with the assortativity coefficient, its evaluation in several real networks and how the properties of the spectral–core can be used to reduce the spectral radius.

Performance of attack strategies on modular networks

Abstract: Vulnerabilities of complex networks have became a trend topic in complex systems recently due to its real world applications. Most real networks tend to be very fragile to high betweenness adaptive attacks. However, recent contributions have shown the importance of interconnected nodes in the integrity of networks and module-based attacks have appeared promising when compared to traditional malicious non-adaptive attacks. In the present work we deeply explore the trade-off associated with attack procedures, introducing a generalized robustness measure and presenting an attack performance index that takes into account both robustness of the network against the attack and the run-time needed to obtained the list of targeted nodes for the attack. Besides, we introduce the concept of deactivation point aimed to mark the point at which the network stops to function properly. We then show empirically that non-adaptive module-based attacks perform better than high degree and betweenness adaptive attacks in networks with well defined community structures and consequent high modularity.

Modelling community formation driven by the status of individual in a society

Abstract: In human societies, people's willingness to compete and strive for better social status as well as being envious of those perceived in some way superior lead to social structures that are intrinsically hierarchical. Here we propose an agent-based, network model to mimic the ranking behaviour of individuals and its possible repercussions in human society. The main ingredient of the model is the assumption that the relevant feature of social interactions is each individual's keenness to maximise his or her status relative to others. The social networks produced by the model are homophilous and assortative, as frequently observed in human communities and most of the network properties seem quite independent of its size. However, it is seen that for small number of agents the resulting network consists of disjoint weakly connected communities while being highly assortative and homophilic. On the other hand larger networks turn out to be more cohesive with larger communities but less homophilic. We find that the reason for these changes is that larger network size allows agents to use new strategies for maximizing their social status allowing for more diverse links between them.

Infection spreading, detection and control in community networks

Abstract: Community structures widely exist in various complex networks. Extensive studies have been carried out on defining and quantifying community structures as well as developing algorithms for detecting them in extra-large complex systems. Despite all these efforts, however, our understanding of why community structures widely exist in so many real-life systems, or in other words, the benefits/drawbacks for real-life systems to have community structures, remains to be rather limited. In this work, we discuss on the effects of community structures on infection propagation, detection and control in complex networks. Specifically, we investigate (i) the effects of community structures on transmission speed and infection size; (ii) when monitors can be deployed in the network to detect the infection spreading, the effects of community structures on early-stage infection detection; and (iii) in adaptive networks with link rewiring for isolating the infected nodes, the effects of community structures on infection control. Our results show that the existence of community structures generally speaking helps slow down the infection spreading; whether it helps reduce the overall infection size when no control method is adopted however depends on the network topology. When infection detection and controlling methods such as link rewiring are adopted, the existence of community structures steadily helps improve the efficiency of infection detection and control, though having too many communities may not necessarily bring along additional benefits.

Betweenness centrality profiles in trees

Abstract: Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The k-betweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most k. The sequence of k-betweenness centralities for all possible values of k forms the betweenness centrality profile of a vertex. We study properties of betweenness centrality profiles in trees. We show that for scale-free random trees, for fixed k, the expectation of k-betweenness centrality strictly decreases as the index of the vertex increases. We also analyze worst-case properties of profiles in terms of the distance of profiles from being monotone, and the number of times pairs of profiles can cross. This is related to whether k-betweenness centrality, for small values of k, may be used instead of having to consider all shortest paths. Bounds are given that are optimal in order of magnitude. We also present some experimental results for scale-free random trees.

Spectral partitioning with blends of eigenvectors

Abstract: Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More generally, we provide pointwise convergence guarantees so that blends (linear combinations) of eigenvectors can be employed to solve data analysis problems with confidence in their accuracy. We demonstrate this theory on an accessible model problem, the Ring of Cliques, by deriving the relevant eigenpairs and comparing the predicted results to numerical solutions. These results bridge the gap between linear algebra based data analysis methods and the convergence theory of iterative approximation methods.

The other fields also exist

Abstract: This was a passionate indictment to the frequent ignorance from the developed North to the problems of the South. But here I want to call the attention to other type of ignorance to which I have been confronted once and again as an Editor, a reviewer or an author of scientific papers in the field of network theory. It is about the ignorance of authors in one discipline to papers published by authors in a different but related area of research. This problem creates an unnecessary duplication of results that contributes to slowing down the healthy development of this field of research. It also contributes to segregate the field into several subfields, in which researchers do the same kind of work, using similar techniques, but without speaking to each other. Network science, the field of our journal, is proud to be a highly interdisciplinary area of research. However, without integration between the different sub-disciplines that contribute to it, the field is not other thing than a fragmented landscape, far from a truly interdisciplinary one. Today, the technology allows us to scan the whole area of research in the blink of an eye. The number of contributions in each topic is huge, and we cannot cover all of them in just a few hours. But, we all, Editors, Reviewers and Authors, have the responsibility of avoiding the ignorance of works that crosses the narrow sub-discipline of the authors and help them to visit the ‘other fields’ that also exists. Just to give one single illustration of what all of this is about I will show a picture (see Fig. 1) of the network of citations of papers containing the phrase ‘Small-World’. It is easy to identify the different subfields that conforms the ‘communities’ in this citation network, but it is not my intention here to make such specific analysis. What it is obvious from this picture, which is worth a thousand words, is that the authors in one sub-discipline hardly cite those in another. Then, when you write your papers, review the papers of others or edit the papers reviewed by others, please be aware that: