Local bow-tie structure of the web

Abstract

Social networks often has the graph structure of giant strongly connected component (GSCC) and its upstream and downstream portions (IN and OUT), known as a bow-tie structure since a pioneering study on the World Wide Web (WWW). GSCC, on the other hand, has community structure, namely tightly knitted clusters, reflecting how the networks developed in time. By using our visualization of enhanced multidimensional scaling (MDS) and force-directed graph drawing for large and directed graphs, we discovered that a bow-tie in the WWW usually has clusters, which are locally-located mini bow-ties that are loosely connected to each other, resulting in a formation of GSCC as a whole. To quantify the mutual connectivity among such local bow-tie, we define a quantity to measure how a local bow-tie connects to others in comparison with random graphs. We found that there are striking difference between the WWW and other social and artificial networks including a million firms' nationwide supply chain network in Japan and thousands of symbols' dependency in the programming language of Emacs LISP, in which a global bow-tie exits. Presumably the difference comes from a self-similar structure and development of the WWW speculated by others.

The Dietary Intake of Carrot-Derived Rhamnogalacturonan-I Accelerates and Augments the Innate Immune and Anti-Viral Interferon Response to Rhinovirus Infection and Reduces Duration and Severity of Symptoms in Humans in a Randomized Trial

“…Innate immune responses are triggered by signaling via pattern-recognition receptors (PRR) such as Toll-like receptors (TLR), double-strand RNA-activated protein kinase R (PKR) and retinoic acid-inducible gene-I (RIG-I)-like receptors that sense pathogen-associated molecular patterns (PAMPs) [6,7]. PRR funnel their signals into interactions with regulated signaling cascades, which then initiate the key antiviral interferon response as well as other common anti-viral and innate immune responses [8,9].…”

Reproducible patterns of neural activity without attractors in cortical networks

“…To perform the tests, we needed information about the firing of neurons, to identify events and cores, and the connections between those neurons, to perform structural analysis of the circuits in which the cores were embedded. Until recently 28 , this double requirement was impossible to fulfill. The MICrONS project 21 now gives this opportunity by releasing electron microscopy (EM) and co-registered two-photon calcium imaging datasets of the same cortical tissue (Fig.…”

“…Given that our data and models are directed, and that our focus is on the flow of information, we identified modules as the most frequented subgraphs spanned by (hundreds of) random walks over directed edges 52 . Once modules were identified, the convergent-divergent bow-tie organization 27,28 of each module was assessed by finding its largest subgraph component (Fig. 3C, inset green), then verifying the existence of an in-component – projecting to the largest (Fig.…”

“…Throughout the cortex, neurons are locally connected in a distance-dependent manner [22][23][24] , which creates modular networks 25,26 . In modular networks, there is a tendency to form converging-diverging connectivity motifs 27,28 , with central nodes characterised by high-flow connections 29,30 . Forcing the activity flow along same pathways would yield reproducible population events.…”

Investigating Fake and Reliable News Sources Using Complex Networks Analysis

“…By modeling the websites and pages on the Web, Broder et al [12] discovered that it has a bow-tie structure, with most accessible pages in a giant strongly connected component (GSCC) and pages that have not been linked yet to the GSCC in the IN or OUT component (the sides of the bow tie). A recent study [13] has shown the presence, on the Web, of local bow-tie structures, as most websites tend to focus on specific topics and content, being able to rely on traffic from loyal online users and frequent visitors.…”