Characterizing the Complexity of Weighted Networks via Graph Embedding and Point Pattern Analysis

Abstract

We propose a new metric to characterize the complexity of weighted complex networks. Weighted complex networks represent a highly organized interactive process, for example, co-varying returns between stocks (financial networks) and coordination between brain regions (brain connectivity networks). Although network entropy methods have been developed for binary networks, the measurement of non-randomness and complexity for large weighted networks remains challenging. We develop a new analytical framework to measure the complexity of a weighted network via graph embedding and point pattern analysis techniques in order to address this unmet need. We first perform graph embedding to project all nodes of the weighted adjacency matrix to a low dimensional vector space. Next, we analyze the point distribution pattern in the projected space, and measure its deviation from the complete spatial randomness. We evaluate our method via extensive simulation studies and find that our method can sensitively detect the difference of complexity and is robust to noise. Last, we apply the approach to a functional magnetic resonance imaging study and compare the complexity metrics of functional brain connectivity networks from 124 patients with schizophrenia and 103 healthy controls. The results show that the brain circuitry is more organized in healthy controls than schizophrenic patients for male subjects while the difference is minimal in female subjects. These findings are well aligned with the established sex difference in schizophrenia.

CoarSAS2hvec: Heterogeneous Information Network Embedding with Balanced Network Sampling

“…The sampling method is further combined with a specifically optimized loss function, forming a new embedding method: CoarSAS2hvec. Future directions include using the method to analyze different systems characterized by HIN, such as the scientific disciplines, the individual careers of scientists, the topic evolution in online forums, and more [50][51][52][53][54]. It is also interesting to explore whether the information entropy can be universally applied to predict the performance of an algorithm.…”

Context- and scale-dependent effects of thymol bioactivity on biological networks: contributions from quail under heat stress

“…For each experimental treatment, we assumed a graph G= { N , E, W }, where N is the set of nodes (27 physiological and behavioral traits), E is the set of links (edges between de the nodes) and W denotes the edges’ weights, as a suitable model of a network [64]. We used a weighted adjacency matrix W NxN to denote the edges’ weights, where an entry w ij is a real number between [0–1] and represents the connectivity strength (absolute value of a Pearson correlation coefficient when P < 0.10) between the two nodes i, j, 0 < j < i < N [64] ( w ij > 0 if a significant correlation exists between nodes i and j , otherwise, w ij = 0). Thus, the location of each nonzero entry in W specifies an edge for the graph, and the weight of the edge is equal to the value of the entry.…”

“…Network entropy provides a robust measurement of the complexity of a weighted graph. It can be used as a descriptive statistic to compare the complexities between networks [64] that, for example, were constructed for two different experimental treatments. Specifically, we estimated the entropy associated with edges' weight.…”

О Распределении Числа Цепочек Специального Вида В Размеченном Полном Графе

“…Для их характеризации используются специально подобранные числовые характеристики, каждая из которых приписывает то или иное свойство каждой из вершин или ребер так называемые веса, а соответствующие графы принято называть взвешенными. Данный тип графов может быть использован в медицине для представления плотности нейронных связей [2,3], в управлении для организации эффективного взаимодействия между командами [4], в урбанистике для демаркации регионов [5].…”