Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

Advances in exponential random graph ( p*) models applied to a large social network

Link prediction based on bipartite networks can not only mine hidden relationships between different types of nodes, but also reveal the inherent law of network evolution. Existing bipartite network link prediction is mainly based on the global structure that cannot analyze the role of the local structure in link prediction. To tackle this problem, this paper proposes a deep link-prediction (DLP) method by leveraging the local structure of bipartite networks. The method first extracts the local structure between target nodes and observes structural information between nodes from a local perspective. Then, representation learning of the local structure is performed on the basis of the graph neural network to extract latent features between target nodes. Lastly, a deep-link prediction model is trained on the basis of latent features between target nodes to achieve link prediction. Experimental results on five datasets showed that DLP achieved significant improvement over existing state-of-the-art link prediction methods. In addition, this paper analyzes the relationship between local structure and link prediction, confirming the effectiveness of a local structure in link prediction.

Network data often contain sensitive relational information. One approach to protecting sensitive information while offering flexibility for network analysis is to share synthesized networks based on the information in originally observed networks. We employ differential privacy (DP) and exponential random graph models (ERGMs) and propose the DP-ERGM method to synthesize network data. We apply DP-ERGM to two real-world networks. We then compare the utility of synthesized networks generated by DP-ERGM, the DyadWise Randomized Response (DWRR) approach, and the Synthesis through Conditional distribution of Edge given nodal Attribute (SCEA) approach. In general, the results suggest that DP-ERGM preserves the original information significantly better than two other approaches in network structural statistics and inference for ERGMs and latent space models. Furthermore, DP-ERGM satisfies node DP through modeling the global network structure with ERGM, a stronger notion of privacy than the edge DP under which DWRR and SCEA operate.

Introduction: Glioma patients show increased global brain network clustering related to poorer cognition and epilepsy. However, it is unclear whether this increase is spatially widespread, localized in the (peri)tumor region only, or decreases with distance from the tumor. Materials and Methods: Weighted global and local brain network clustering was determined in 71 glioma patients and 53 controls by using magnetoencephalography. Tumor clustering was determined by averaging local clustering of regions overlapping with the tumor, and vice versa for non-tumor regions. Euclidean distance was determined from the tumor centroid to the centroids of other regions. Results: Patients showed higher global clustering compared with controls. Clustering of tumor and non-tumor regions did not differ, and local clustering was not associated with distance from the tumor. Post hoc analyses revealed that in the patient group, tumors were located more often in regions with higher clustering in controls, but it seemed that tumors of patients with high global clustering were located more often in regions with lower clustering in controls. Conclusions: Glioma patients show non-local network disturbances. Tumors of patients with high global clustering may have a preferred localization, namely regions with lower clustering in controls, suggesting that tumor localization relates to the extent of network disruption. Impact statement This work uses the innovative framework of network neuroscience to investigate functional connectivity patterns associated with brain tumors. Glioma (primary brain tumor) patients experience cognitive deficits and epileptic seizures, which have been related to brain network alterations. This study shows that glioma patients have a spatially widespread increase in global network clustering, which cannot be attributed to local effects of the tumor. Moreover, tumors occur more often in brain regions with higher network clustering in controls. This study emphasizes the global character of network alterations in glioma patients and suggests that preferred tumor locations are characterized by particular network profiles.

In recent years, a great number of Somalis are involuntarily displaced within the country. However, we do not fully understand what and how climatic, environmental, and socio-political drivers push internally displaced persons (IDPs). Among several climatic drivers, what is statistically significant to internal displacement? Is the drought intensity alone a key driver of displacement? Are social network structures important in displacement decisions? To provide quantitative evidence, we developed a bootstrapping temporal exponential random graph model (bTERGM) for internal displacement decisions in Somalia. We used the Protection and Return Monitoring Network dataset with drought indices based on precipitation, temperature, and vegetation from the Somali Water and Land Information Management. We found that IDPs tend to consider both the intensity and successiveness of droughts based on precipitation, temperature, or vegetation. The Intensity of each component alone was not a significant driver for Somali IDPs. Local network structures were not very significant in the temporal model at the monthly scale, while previous displacement experience played a critical role in IDP movements. Our results help us better understand the displacement decision-making process so that policymakers can predict IDP movements and establish adequate policies.

Network influences on the development and implementation of active transportation policies in six U.S. cities

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms for mining communities have focused on global graph structure, and often run in time proportional to the size of the entire graph. As we explore networks with millions of vertices and find communities of size in the hundreds, it becomes important to shift our attention from macroscopic structure to microscopic structure in large networks. A growing body of work has been adopting local expansion methods in order to identify communities from a few exemplary seed members. In this article, we propose a novel approach for finding overlapping communities called L emon ( L ocal E xpansion via M inimum O ne N orm). Provided with a few known seeds , the algorithm finds the community by performing a local spectral diffusion. The core idea of L emon is to use short random walks to approximate an invariant subspace near a seed set, which we refer to as local spectra . Local spectra can be viewed as the low-dimensional embedding that captures the nodes’ closeness in the local network structure. We show that L emon ’s performance in detecting communities is competitive with state-of-the-art methods. Moreover, the running time scales with the size of the community rather than that of the entire graph. The algorithm is easy to implement and is highly parallelizable. We further provide theoretical analysis of the local spectral properties, bounding the measure of tightness of extracted community using the eigenvalues of graph Laplacian. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the seed set quality and quantity would affect the performance are provided.

Social network analysis is a suite of approaches for exploring relational data. Two approaches commonly used to analyze animal social network data are permutation-based tests of significance and exponential random graph models. However, the performance of these approaches when analyzing different types of network data has not been simultaneously evaluated. Here we test both approaches to determine their performance when analyzing a range of biologically realistic simulated animal social networks. We examined the false positive and false negative error rate of an effect of a two-level explanatory variable (e.g., sex) on the number and combined strength of an individual’s network connections. We measured error rates for two types of simulated data collection methods in a range of network structures, and with/without a confounding effect and missing observations. Both methods performed consistently well in networks of dyadic interactions, and worse on networks constructed using observations of individuals in groups. Exponential random graph models had a marginally lower rate of false positives than permutations in most cases. Phenotypic assortativity had a large influence on the false positive rate, and a smaller effect on the false negative rate for both methods in all network types. Aspects of within- and between-group network structure influenced error rates, but not to the same extent. In "grouping event-based" networks, increased sampling effort marginally decreased rates of false negatives, but increased rates of false positives for both analysis methods. These results provide guidelines for biologists analyzing and interpreting their own network data using these methods.

Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

Exponential random graph models (ERGMs) are increasingly applied to observed network data and are central to understanding social structure and network processes. The chapters in this edited volume provide a self-contained, exhaustive account of the theoretical and methodological underpinnings of ERGMs, including models for univariate, multivariate, bipartite, longitudinal and social-influence type ERGMs. Each method is applied in individual case studies illustrating how social science theories may be examined empirically using ERGMs. The authors supply the reader with sufficient detail to specify ERGMs, fit them to data with any of the available software packages and interpret the results.

Synthetic power grids enable real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using exponential random graph (ERG) models. Our two main contributions are (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify edge counts per bus type and k-triangles as crucial topological characteristics for synthetic power-grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids. Published by the American Physical Society 2024

Analyses of alterations of brain networks have gained an increasing interest in stroke rehabilitation research. Compared with functional networks derived from resting-state analyses, there is limited knowledge of how structural network topology might undergo changes after stroke and, more importantly, if structural network information obtained early after stroke could enhance recovery models to infer later outcomes. The present work re-analysed cross-sectional structural imaging data, obtained within the first 2 weeks, of 45 acute stroke patients (22 females, 24 right-sided strokes, age 68 ± 13 years). Whole-brain tractography was performed to reconstruct structural connectomes and graph-theoretical analyses were employed to quantify global network organization with a focus on parameters of network integration and modular processing. Graph measures were compared between stroke patients and 34 healthy controls (15 females, aged 69 ± 10 years) and they were integrated with four clinical scores of the late subacute stage, covering neurological symptom burden (National Institutes of Health Stroke Scale), global disability (modified Rankin Scale), activity-related disability (Barthel Index) and motor functions (Upper-Extremity Score of the Fugl-Meyer Assessment). The analyses were employed across the complete cohort and, based on clustering analysis, separately within subgroups stratified in mild to moderate (n = 21) and severe (n = 24) initial deficits. The main findings were (i) a significant reduction of network’s global efficiency, specifically in patients with severe deficits compared with controls (P = 0.010) and (ii) a significant negative correlation of network efficiency with the extent of persistent functional deficits at follow-up after 3–6 months (P ≤ 0.032). Specifically, regression models revealed that this measure was capable to increase the explained variance in future deficits by 18% for the modified Rankin Scale, up to 24% for National Institutes of Health Stroke Scale, and 16% for Barthel Index when compared with models including the initial deficits and the lesion volume. Patients with mild to moderate deficits did not exhibit a similar impact of network efficiency on outcome inference. Clustering coefficient and modularity, measures of segregation and modular processing, did not exhibit comparable structure–outcome relationships, neither in severely nor in mildly affected patients. This study provides empirical evidence that structural network efficiency as a graph-theoretical marker of large-scale network topology, quantified early after stroke, relates to recovery. Notably, this contribution was only evident in severely but not mildly affected stroke patients. This suggests that the initial clinical deficit might shape the dependency of recovery on global network topology after stroke.

Background: Cognitive control has been linked to both the microstructure of individual tracts and the structure of whole-brain networks, but their relative contributions in health and disease remain unclear.Objective: To determine the contribution of both localized white matter tract damage and disruption of global network architecture to cognitive control, in older age and Mild Cognitive Impairment (MCI).Materials and Methods: Twenty-five patients with MCI and 20 age, sex, and intelligence-matched healthy volunteers were investigated with 3 Tesla structural magnetic resonance imaging (MRI). Cognitive control and episodic memory were evaluated with established tests. Structural network graphs were constructed from diffusion MRI-based whole-brain tractography. Their global measures were calculated using graph theory. Regression models utilized both global network metrics and microstructure of specific connections, known to be critical for each domain, to predict cognitive scores.Results: Global efficiency and the mean clustering coefficient of networks were reduced in MCI. Cognitive control was associated with global network topology. Episodic memory, in contrast, correlated with individual temporal tracts only. Relationships between cognitive control and network topology were attenuated by addition of single tract measures to regression models, consistent with a partial mediation effect. The mediation effect was stronger in MCI than healthy volunteers, explaining 23-36% of the effect of cingulum microstructure on cognitive control performance. Network clustering was a significant mediator in the relationship between tract microstructure and cognitive control in both groups.Conclusion: The status of critical connections and large-scale network topology are both important for maintenance of cognitive control in MCI. Mediation via large-scale networks is more important in patients with MCI than healthy volunteers. This effect is domain-specific, and true for cognitive control but not for episodic memory. Interventions to improve cognitive control will need to address both dysfunction of local circuitry and global network architecture to be maximally effective.

Algorithmic and modeling advances in the area of protein-protein interaction (PPI) network analysis could contribute to the understanding of biological processes. Local structure of networks can be measured by the frequency distribution of graphlets, small connected non-isomorphic induced subgraphs. This measure of local structure has been used to show that high-confidence PPI networks have local structure of geometric random graphs. Finding graphlets exhaustively in a large network is computationally intensive. More complete PPI networks, as well as PPI networks of higher organisms, will thus require efficient heuristic approaches. We propose two efficient and scalable heuristics for finding graphlets in high-confidence PPI networks. We show that both PPI and their model geometric random networks, have defined boundaries that are sparser than the 'inner parts' of the networks. In addition, these networks exhibit 'uniformity' of local structure inside the networks. Our first heuristic exploits these two structural properties of PPI and geometric random networks to find good estimates of graphlet frequency distributions in these networks up to 690 times faster than the exhaustive searches. Our second heuristic is a variant of a more standard sampling technique and it produces accurate approximate results up to 377 times faster than the exhaustive searches. We indicate how the combination of these approaches may result in an even better heuristic. Supplementary information is available at http://www.cs.toronto.edu/~natasha/BIOINF-2005-0946/Supplementary.pdf. Software implementing the algorithms is available at http://www.cs.toronto.edu/~natasha/BIOINF-2005-0946/estimate_grap-hlets.html. Supplementary data are available at Bioinformatics online.

Whole-brain network analysis is commonly used to investigate the topology of the brain using a variety of neuroimaging modalities. This approach is notable for its applicability to a large number of domains, such as understanding how brain network organization relates to cognition and behavior and examining disrupted brain network organization in disease. A benefit to this approach is the ability to summarize overall brain network organization with a single metric (e.g., global efficiency). However, important local differences in network structure might exist without any corresponding observable differences in global topology, making a whole-brain analysis strategy unlikely to detect relevant local findings. Conversely, using local network metrics can identify local differences, but are not directly informative of differences in global topology. Here, we propose the network statistic (NS) jackknife framework, a simulated lesioning method that combines the utility of global network analysis strategies with the ability to detect relevant local differences in network structure. We evaluate the NS jackknife framework with a simulation study and an empirical example comparing global efficiency in children with attention-deficit/hyperactivity disorder (ADHD) and typically developing (TD) children. The NS jackknife framework has been implemented in a public, open-source R package, netjack, available at https://cran.r-project.org/package=netjack.