Random intersection graphs with communities

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of communities and individuals, where these communities may overlap. We generalize the model, allowing for arbitrary community structures within the communities. In our new model, communities may overlap, and they have their own internal structure described by arbitrary finite community graphs. Our model turns out to be tractable. We analyze the overlapping structure of the communities, show local weak convergence (including convergence of subgraph counts), and derive the asymptotic degree distribution and the local clustering coefficient.

Structure and Evolution of the International Pesticide Trade Networks

To meet the increasing demand for food around the world, pesticides are widely used and will continue to be widely used in agricultural production to reduce yield losses and maintain product quality. International pesticide trade serves to reallocate the distribution of pesticides around the world. We investigate the statistical properties of the international trade networks of five categories of pesticides from the view angle of temporal directed and weighted networks. We observed an overall increasing trend in network size, network density, average in- and out-degrees, average in- and out-strengths, temporal similarity, and link reciprocity, indicating that the rising globalization of pesticides trade is driving the networks denser. However, the distributions of link weights remain unchanged along time for the five categories of pesticides. In addition, all the networks are disassortatively mixed because large importers or exporters are more likely to trade with small exporters or importers. We also observed positive correlations between in-degree and out-degree, in-strength and out-strength, link reciprocity and in-degree, out-degree, in-strength, and out-strength, while node’s local clustering coefficient is negatively related to in-degree, out-degree, in-strength, and out-strength. We show that some structural and dynamic properties of the international pesticide trade networks are different from those of the international trade networks, highlighting the presence of idiosyncratic features of different goods and products in the international trade.

Overlapping Structures Detection in Protein-Protein Interaction Networks Using Community Detection Algorithm Based on Neighbor Clustering Coefficient

With the rapid development of bioinformatics, researchers have applied community detection algorithms to detect functional modules in protein-protein interaction (PPI) networks that can predict the function of unknown proteins at the molecular level and further reveal the regularity of cell activity. Clusters in a PPI network may overlap where a protein is involved in multiple functional modules. To identify overlapping structures in protein functional modules, this paper proposes a novel overlapping community detection algorithm based on the neighboring local clustering coefficient (NLC). The contributions of the NLC algorithm are threefold: (i) Combine the edge-based community detection method with local expansion in seed selection and the local clustering coefficient of neighboring nodes to improve the accuracy of seed selection; (ii) A method of measuring the distance between edges is improved to make the result of community division more accurate; (iii) A community optimization strategy for the excessive overlapping nodes makes the overlapping structure more reasonable. The experimental results on standard networks, Lancichinetti-Fortunato-Radicchi (LFR) benchmark networks and PPI networks show that the NLC algorithm can improve the Extended modularity (EQ) value and Normalized Mutual Information (NMI) value of the community division, which verifies that the algorithm can not only detect reasonable communities but also identify overlapping structures in networks.

On the usefulness of graph-theoretic properties in the study of perceived numerosity

Observers can quickly estimate the quantity of sets of visual elements. Many aspects of this ability have been studied and the underlying process has been called the Approximate Number Sense (Dehaene, 2011). Estimates can be biased by specific visual properties, such as size and clustering of the elements. For intermediate numerical quantities and low density (above five, but before texturisation), human performance can be predicted by a model based on the region of influence of elements (occupancy model: (Allïk & Tuulmets, 1991). We include ten indices based on graph theory, and we compare them with the occupancy model: independence number, domination, connected components, local clustering coefficient, global clustering coefficient, random walk, eigenvector centrality, maximum clique, total degree of connectivity, and total edge length. We carried out comparisons across a range of parameters, and we varied the size of the region of influence around an element. The analysis of the pattern of correlations suggests two main groups of measures. The first of these is sensitive to presence of clustering of elements, the second seemed more sensitive to how information spreads in graphs. Empirical work on perception of numerosity may benefit from comparing or controlling for these properties.

EEG Source Network for the Diagnosis of Schizophrenia and the Identification of Subtypes Based on Symptom Severity—A Machine Learning Approach

A precise diagnosis and a comprehensive assessment of symptom severity are important clinical issues in patients with schizophrenia (SZ). We investigated whether electroencephalography (EEG) features obtained from EEG source network analyses could be effectively applied to classify the SZ subtypes based on symptom severity. Sixty-four electrode EEG signals were recorded from 119 patients with SZ (53 males and 66 females) and 119 normal controls (NC, 51 males and 68 females) during resting-state with closed eyes. Brain network features (global and local clustering coefficient and global path length) were calculated from EEG source activities. According to positive, negative, and cognitive/disorganization symptoms, the SZ patients were divided into two groups (high and low) by positive and negative syndrome scale (PANSS). To select features for classification, we used the sequential forward selection (SFS) method. The classification accuracy was evaluated using 10 by 10-fold cross-validation with the linear discriminant analysis (LDA) classifier. The best classification accuracy was 80.66% for estimating SZ patients from the NC group. The best classification accuracy between low and high groups in positive, negative, and cognitive/disorganization symptoms were 88.10%, 75.25%, and 77.78%, respectively. The selected features well-represented the pathological brain regions of SZ. Our study suggested that resting-state EEG network features could successfully classify between SZ patients and the NC, and between low and high SZ groups in positive, negative, and cognitive/disorganization symptoms.

Analysis and synthesis of a growing network model generating dense scale-free networks via category theory

We propose a growing network model that can generate dense scale-free networks with an almost neutral degree−degree correlation and a negative scaling of local clustering coefficient. The model is obtained by modifying an existing model in the literature that can also generate dense scale-free networks but with a different higher-order network structure. The modification is mediated by category theory. Category theory can identify a duality structure hidden in the previous model. The proposed model is built so that the identified duality is preserved. This work is a novel application of category theory for designing a network model focusing on a universal algebraic structure.

Examining association between cohesion and diversity in collaboration networks of pharmaceutical clinical trials with drug approvals

Objective Clinical trials ensure that pharmaceutical treatments are safe, efficacious, and effective for public consumption, but are extremely complex, taking up to 10 years and $2.6 billion to complete. One main source of complexity arises from the collaboration between actors, and network science methodologies can be leveraged to explore that complexity. We aim to characterize collaborations between actors in the clinical trials context and investigate trends of successful actors. Materials and Methods We constructed a temporal network of clinical trial collaborations between large and small-size pharmaceutical companies, academic institutions, nonprofit organizations, hospital systems, and government agencies from public and proprietary data and introduced metrics to quantify actors’ collaboration network structure, organizational behavior, and partnership characteristics. A multivariable regression analysis was conducted to determine the metrics’ relationship with success. Results We found a positive correlation between the number of successful approved trials and interdisciplinary collaborations measured by a collaboration diversity metric (P < .01). Our results also showed a negative effect of the local clustering coefficient (P < .01) on the success of clinical trials. Large pharmaceutical companies have the lowest local clustering coefficient and more diversity in partnerships across biomedical specializations. Conclusions Large pharmaceutical companies are more likely to collaborate with a wider range of actors from other specialties, especially smaller industry actors who are newcomers in clinical research, resulting in exclusive access to smaller actors. Future investigations are needed to show how concentrations of influence and resources might result in diminished gains in treatment development.

Words, constructions and corpora: Network representations of constructional semantics for Mandarin space particles

In this study, we aim to demonstrate the effectiveness of network science in exploring the emergence of constructional semantics from the connectedness and relationships between linguistic units. With Mandarin locative constructions (MLCs) as a case study, we extracted constructional tokens from a representative corpus, including their respective space particles (SPs) and the head nouns of the landmarks (LMs), which constitute the nodes of the network. We computed edges based on the lexical similarities of word embeddings learned from large text corpora and the SP-LM contingency from collostructional analysis. We address three issues: (1) For each LM, how prototypical is it of the meaning of the SP? (2) For each SP, how semantically cohesive are its LM exemplars? (3) What are the emerging semantic fields from the constructional network of MLCs? We address these questions by examining the quantitative properties of the network at three levels: microscopic (i.e., node centrality and local clustering coefficient), mesoscopic (i.e., community) and macroscopic properties (i.e., small-worldness and scale-free). Our network analyses bring to the foreground the importance of repeated language experiences in the shaping and entrenchment of linguistic knowledge.

Counting Triangles in Power-Law Uniform Random Graphs

We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two random neighbors of a vertex of degree $k$ are connected. We find that the number of triangles, as well as the local clustering coefficient, scale similarly as in the erased configuration model, where all self-loops and multiple edges of the configuration model are removed. Interestingly, uniform random graphs contain more triangles than erased configuration models with the same degree sequence. The number of triangles in uniform random graphs is closely related to that in a version of the rank-1 inhomogeneous random graph, where all vertices are equipped with weights, and the probabilities that edges are present are moderated by asymptotically linear functions of the products of these vertex weights.

Characterizing several properties of high-dimensional random Apollonian networks

In this article, we investigate several properties of high-dimensional random Apollonian networks, including two types of degree profiles, the small-world effect (clustering property), sparsity and three distance-based metrics. The characterizations of the degree profiles are based on several rigorous mathematical and probabilistic methods, such as a two-dimensional mathematical induction, analytic combinatorics and Pólya urns, etc. The small-world property is uncovered by a well-developed measure—local clustering coefficient and the sparsity is assessed by a proposed Gini index. Finally, we look into three distance-based properties; they are total depth, diameter and Wiener index.