Temporal Degree-Degree and Closeness-Closeness: A New Centrality Metrics for Social Network Analysis

In the area of network analysis, centrality metrics play an important role in defining the “most important” actors in a social network. However, nowadays, most types of networks are dynamic, meaning their topology changes over time. The connection weights and the strengths of social links between nodes are an important concept in a social network. The new centrality measures are proposed for weighted networks, which relies on a time-ordered weighted graph model, generalized temporal degree and closeness centrality. Furthermore, two measures—Temporal Degree-Degree and Temporal Closeness-Closeness—are employed to better understand the significance of nodes in weighted dynamic networks. Our study is caried out according to real dynamic weighted networks dataset of a university-based karate club. Through extensive experiments and discussions of the proposed metrics, our analysis proves that there is an effectiveness on the impact of each node throughout social networks.

Optimizing weighted gene co-expression network analysis with a multi-threaded calculation of the topological overlap matrix

Biomolecular networks are often assumed to be scale-free hierarchical networks. The weighted gene co-expression network analysis (WGCNA) treats gene co-expression networks as undirected scale-free hierarchical weighted networks. The WGCNA R software package uses an Adjacency Matrix to store a network, next calculates the topological overlap matrix (TOM), and then identifies the modules (sub-networks), where each module is assumed to be associated with a certain biological function. The most time-consuming step of WGCNA is to calculate TOM from the Adjacency Matrix in a single thread. In this paper, the single-threaded algorithm of the TOM has been changed into a multi-threaded algorithm (the parameters are the default values of WGCNA). In the multi-threaded algorithm, Rcpp was used to make R call a C++ function, and then C++ used OpenMP to start multiple threads to calculate TOM from the Adjacency Matrix. On shared-memory MultiProcessor systems, the calculation time decreases as the number of CPU cores increases. The algorithm of this paper can promote the application of WGCNA on large data sets, and help other research fields to identify sub-networks in undirected scale-free hierarchical weighted networks. The source codes and usage are available at https://github.com/do-somethings-haha/multi-threaded_calculate_unsigned_TOM_from_unsigned_or_signed_Adjacency_Matrix_of_WGCNA.

New Betweenness Centrality Node Attack Strategies for Real-World Complex Weighted Networks

In this work, we introduce a new node attack strategy removing nodes with the highest conditional weighted betweenness centrality (CondWBet), which combines the weighted structure of the network and the node’s conditional betweenness. We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network, in addition to the commonly used binary-topological measure, i.e., the largest connected cluster (LCC). We find that if the measure is WEFF, the CondWBet strategy is the best to decrease WEFF in 3 out of 5 cases. Further, CondWBet is the most effective strategy to reduce WEFF at the beginning of the removal process, whereas the Strength that removes nodes with the highest sum of the link weights first shows the highest efficacy in the final phase of the removal process when the network is broken into many small clusters. These last outcomes would suggest that a better attacking in weighted networks strategy could be a combination of the CondWBet and Strength strategies.

On the statistical significance of communities from weighted graphs

Community detection is a fundamental procedure in the analysis of network data. Despite decades of research, there is still no consensus on the definition of a community. To analytically test the realness of a candidate community in weighted networks, we present a general formulation from a significance testing perspective. In this new formulation, the edge-weight is modeled as a censored observation due to the noisy characteristics of real networks. In particular, the edge-weights of missing links are incorporated as well, which are specified to be zeros based on the assumption that they are truncated or unobserved. Thereafter, the community significance assessment issue is formulated as a two-sample test problem on censored data. More precisely, the Logrank test is employed to conduct the significance testing on two sets of augmented edge-weights: internal weight set and external weight set. The presented approach is evaluated on both weighted networks and un-weighted networks. The experimental results show that our method can outperform prior widely used evaluation metrics on the task of individual community validation.