The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Abstract

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.aggregation ͉ subgraphs A number of complex biological and nonbiological networks were recently found to contain network motifs, representing elementary interaction patterns between small groups of nodes (subgraphs) that occur substantially more often than would be expected in a random network of similar size and connectivity (1, 2). Theoretical and experimental evidence indicates that at least some of these recurring elementary interaction patterns carry significant information about the given network's function and overall organization (1-4). For example, transcriptional regulatory networks of cells (1, 2, 5, 6), neural networks of C. elegans (2), and some electronic circuits (2) are all information processing networks that contain a significant number of feed-forward loop (FFL) motifs. However, in transcriptional regulatory networks these motifs do not exist in isolation but meld into motif clusters (7), while other networks are devoid of FFLs altogether (2).In general, all subgraphs have two important properties: their topology and the directionality of their links. In cellular networks, these two properties can be clearly separated from each other. In protein-protein interaction (PPI) networks all links are by definition nondirectional. In contrast, in transcriptional regulatory networks information flow between a transcription factor and the operon (gene) regulated by it is almost always unidirectional (1, 2). Metabolic networks occupy an intermediate position between these two extremes, because most, but not all, metabolic reactions are reversible under various growth conditions. Despite the difference in the relative role of link directionality, the large-scale organization of the three different network types is quite similar, most being characterized by a scale-free connectivity distribution and hierarchical modularity (8-12). The only exception is the incoming degree distribution (i.e., the number of transcription factors regulating a target gene) of regulatory...

Enrichment and aggregation of topological motifs are independent organizational principles of integrated interaction networks

“…Several studies have further investigated the connection between network motif enrichment and aggregation, from a topological as well as from an evolutionary perspective. In hierarchical scale-free random networks the enrichment and aggregation of a certain class of subgraphs are intimately related to each other and to the global topological network parameters 11 . Furthermore these subgraphs tend to aggregate around network hubs 11 .…”

“…In hierarchical scale-free random networks the enrichment and aggregation of a certain class of subgraphs are intimately related to each other and to the global topological network parameters 11 . Furthermore these subgraphs tend to aggregate around network hubs 11 . A comparative phylogenetic analysis of genes within motifs has shown that they are not subject to any evolutionary pressure to preserve the motif pattern 12 .…”

Construction of Complex Network with Multiple Time Series Relevance

“…Recently, there has been a growing industry in the application of complex network theory to carry out time series analysis [23,24]. The time series firstly is transformed into networks and then analyzed with various complex network tools [25][26][27][28]. Shirazi et al [29] demonstrated that the time series can be reconstructed with high precision by means of a simple random walk on their corresponding networks.…”

Revealing intricate properties of communities in the bipartite structure of online social networks

“…This approach have proven to be useful to identify non trivial properties of the structure of networks in very different contexts. We can cite for instance computer networks (like the Internet, peer-to-peer systems, the web) [1], [2], biological networks (protein-protein interaction networks, metabolic processes) [3], [4], social networks (friendship networks, co-publication networks) [3], [5], legal networks [6], linguistics [7], economy [8], etc.…”