Networks describe a variety of interacting complex systems in social science, biology and information technology. Usually the nodes of real networks are identified not only by their connections but also by some other characteristics. Examples of characteristics of nodes can be age, gender or nationality of a person in a social network, the abundance of proteins in the cell taking part in a protein-interaction networks or the geographical position of airports that are connected by directed flights. Integrating the information on the connections of each node with the information about its characteristics is crucial to discriminating between the essential and negligible characteristics of nodes for the structure of the network. In this paper we propose a general indicator, based on entropy measures, to quantify the dependence of a network's structure on a given set of features.
We apply this method to social networks of friendships in US schools, to the protein-interaction network of Saccharomyces cerevisiae and to the US airport network, showing that the proposed measure provides information which complements other known measures.
In this paper, we perform the initial and comprehensive study on the problem of measuring node relevance on signed social networks. We design numerous relevance measurements for signed social networks from both local and global perspectives and investigate the connection between signed relevance measurements, balance theory and signed network properties. Experimental results are conducted to study the effects of signed relevance measurements with four real-world datasets on signed network analysis tasks.
Which nodes are most vulnerable to an epidemic spreading through a network, and which carry the highest risk of causing a major outbreak if they are the source of the infection? Here we show how these questions can be answered to good approximation using the cavity method. Several curious properties of node vulnerability and risk are explored: some nodes are more vulnerable than others to weaker infections, yet less vulnerable to stronger ones; a node is always more likely to be caught in an outbreak than it is to start one, except when the disease has a deterministic lifetime; the rank order …
We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the ability of a node to acquire links is affected by its degree, its fitness, as well as its relevance which typically decays over time. After a review of existing models, we argue that they cannot explain the above-mentioned two properties (1) and (2) at the same time. We have found that apart from being empirically observed in many systems, the exponential g…
Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis. To this end,we examine the effect of fixing the strength sequence in multi-edge networks on several network observables such as degrees, disparity, average neighbor properties and weight distribution using an ensemble approach. We provide a general method to calculate any desired weighted network metric and we show that several features detected in real data c…
In recent years, community structure has emerged as a key component of complex network analysis. As more data has been collected, researchers have begun investigating changing community structure across multiple networks. Several methods exist to analyze changing communities, but most of these are limited to evolution of a single network over time. In addition, most of the existing methods are more concerned with change at the community level than at the level of the individual node. In this paper, we introduce scaled inclusivity, which is a method to quantify the change in community structure…
In ATM systems, the massive number of interacting entities makes it difficult to identify critical elements and paths of disturbance propagation, as well as to predict the system-wide effects that innovations might have. To this end, suitable metrics are required to assess the role of the interconnections between the elements and complex network science provides several network metrics to evaluate the network functioning. Here we focus on centrality and causality metrics measuring, respectively, the importance of a node and the propagation of disturbances along links. By investigating a datase…
The fluctuation of dynamic variables in complex networks is known to depend on the dimension and the heterogeneity of the substrate networks. Previous studies, however, have reported inconsistent results for the scaling behavior of fluctuation in strongly heterogeneous networks. To understand the origin of this conflict, we study the dynamic fluctuation on scale-free networks with a common small degree exponent but different mean degrees and minimum degrees constructed by using the configuration model and the static model. It turns out that the global fluctuation of dynamic variables diverges …
We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity of information lost when pairs of nodes are iteratively merged. We show how this measure is able to quantify several meso-scale structures, like the presence of modularity, bipartite and core-periphery configurations, or motifs. Results corresponding to a large set of real networks are used to validate its ability to detect non-trivial topological patterns.
In this paper we investigate a susceptible-infected-susceptible (SIS) epidemic model describing data dissemination in opportunistic networks with heterogeneous setting of transmission parameters. We obtained the estimation of the final epidemic size assuming that amount of data transferred between network nodes possesses a Pareto distribution, implying scale-free properties. In this context, more heterogeneity in susceptibility means the less severe epidemic progression, and, on the contrary, more heterogeneity in infectivity leads to more severe epidemics -- assuming that the other parameter …
Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To a…
Recently it has been recognized that many complex social, technological and biological networks have a multilayer nature and can be described by multiplex networks. Multiplex networks are formed by a set of nodes connected by links having different connotations forming the different layers of the multiplex. Characterizing the centrality of the nodes in a multiplex network is a challenging task since the centrality of the node naturally depends on the importance associated to links of a certain type. Here we propose to assign to each node of a multiplex network a centrality called Functional Mu…
Many real-world networks are large, complex and thus hard to understand, analyze or visualize. The data about networks is not always complete, their structure may be hidden or they change quickly over time. Therefore, understanding how incomplete system differs from complete one is crucial. In this paper, we study the changes in networks under simplification (i.e., reduction in size). We simplify 30 real-world networks with six simplification methods and analyze the similarity between original and simplified networks based on preservation of several properties, for example degree distribution,…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component connecting large portion of the network would emerge. Assessing the percolation threshold of networks has wide applications in network reliability, information spread, epidemic control, etc. The theoretical approach so far to assess the percolation threshold is mainly based on spectral radius of adjacency matrix or non-backtracking matrix, which is limited to dense …
Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This breaks down when there are nodes with no edges, persisting or otherwise. The following outlines a proposed correction to ensure that correlation metrics have the expected behavior.
Technische Universität Dresden（德累斯顿工业大学）；Tsinghua University（清华大学）
Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation of this data derived by real complex physical systems. In the hyperbolic space, the radial coordinate of the nodes characterizes their hierarchy, whereas the angular distance between them represents their similarity. Several studies have highlighted the relationship between the an…
We study network centrality based on dynamic influence propagation models in social networks. To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static network structures, we focus on two basic centrality measures: (a) Single Node Influence (SNI) centrality, which measures each node's significance by its influence spread; and (b) Shapley Centrality, which uses the Shapley value of the influence spread function --- formulated based on a fundamental cooperative-game-theoretical concept --- to measure …
Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of a node is derived from the importance of its neighboring nodes. For directed and weighted complex networks, where the nodes can carry some intrinsic property value, there have been centrality measures proposed that are variants of eigenvector centrality. However, these expressions all suffer from shortcomings. Here, an extension of such centrality measures …
