Relaxed Clique Percolation and Disinformation-Resilient Domains for Social Commerce Networks

TL;DR

It is shown how a platform can limit this risk by exploiting the social link structure between its nodes without the need to know which nodes are good or bad citizens, and introduces Relaxed Clique Percolation (RCP), a class of policies to compose personalized disinformation-resilient domains.

Abstract

Must we trace and block all fake content in a social commerce network so that genuine users may enjoy fake-free information? Such efforts largely fail, because, as we get better at spam detection, spammers use the same advances for anti-detection. As a fundamentally new approach, we show that an online platform can aggregate and route user-generated content in a smart personalized way, which fosters and relies on "collective social responsibility". We introduce the notion of information aggregation domain, or simply, domain: composed for a given "central" node (user account), a domain is a connected set of nodes whose user-generated content is eligible to be used to meet the central node's information needs. Admitting malicious information sources - "bad citizen" nodes - into "good citizen" nodes' domains puts the good citizens at risk for disinformation attacks. We show how a platform can limit this risk by exploiting the social link structure between its nodes without the need to know which nodes are good or bad citizens. We introduce Relaxed Clique Percolation (RCP), a class of policies to compose personalized disinformation-resilient domains. Then, we define "RCP cores" and show how they can be used to efficiently compose resilient domains for all network nodes at once. Finally, we analyze the properties of RCP domains found in real-world social networks including Slashdot, Facebook, Flickr, and Yelp, to affirm that in practice, RCP domains turn out to be large and spatially diverse.

Figures (7)

• Figure 1: (a) Concept of a resilient domain composed for a "central" node $i$. It is large (extends far), contains mostly good citizens, and bars mass-infiltration of bad citizens. Naturally, the direct neighbors of $i$ are first to get admitted into the domain. (b) Key assumption of socially responsible behavior: while a good citizen can occasionally make a mistake and link with a bad citizen, the case where a well-communicating group of good citizens holds the same bad citizen as friend is extremely unlikely.
• Figure 2: Schematic illustration of one expansion of a backbone in Step 1 of RCP policy $\pi$. (a) The expansion feasibility properties $\textbf{P}^{\pi}=\{P^{\pi}_1, P^{\pi}_2, P^{\pi}_3\}$ impose necessary conditions on the specification duplet $(R,Q)$: $\{P^{\pi}_1 \}$ restricts $R\cup Q$ to be a relaxed clique that possesses both reachability and familiarity properties; $\{P^{\pi}_2 \}$ restricts set $R$ to be well-rooted in the rest of the domain; and $\{ P^{\pi}_3 \}$ restricts set $Q$ to be well-connected with set $R$. For example, in order to satisfy $P^{\pi(\alpha,\beta)}$ with $\alpha=4$ and $\beta=3$, set $R$ must have at least 4 connected nodes that have a common friend with set $Q$, or each node in $Q$ must have at least 3 mutual friends with a node in $R$.
• Figure 3: (a) Examples of strong ties. In the picture, the links of strength 3 are depicted as double blue lines; (b) Schematic illustration of a sequential process of composing a backbone of a $\pi$-compliant-domain under some the RCP policy $\pi(\alpha,\beta)$ with parameters $\alpha=4$ and $\beta=3$. The regions bounded by dotted lines are feasible expansions as per $\textbf{P}^{\pi}=\{P^{\pi}_1, P^{\pi}_2, P^{\pi}_3\}$; (c) The complete domain with the backbone in (b).
• Figure 4: Illustration of the method for composing $\pi(\alpha, \beta)$-compliant complete domain from graph $G$ using the directed graph of RCP-supercore. Figure (a) shows an original social graph; in it, the $\beta$-strong ties are highlighted. These strong ties form new, strongly connected components of the graph shown using dotted circles. Figure (b) shows these components in the original network. The components have the nodes from original network $G$ (the edges are omitted in this simplistic view); special connections between the components (edges in the RCP-supercore-digraph) are represented by arrows. Figure (c) shows that all the components in (b) that are part of cycles are merged together; the resultant elements of the graph are all $\pi$-supercores. Figure (d) shows how one can compose $\pi$-compliant complete domains from the graph in (c): the directed paths indicate which $\pi$-supercores form the largest $\pi$-compliant backbones for the nodes of the original graph that they (the $\pi$-supercores) contain.
• Figure 5: Fraction of all nodes of the network of each dataset with fixed degree that have large $\pi(\alpha, \beta)$-compliant complete domains (of size of at least $1000$ nodes) composed for them. The RCP policy parameters are varied: $\beta = 3,4,...,10$ and $\alpha = \beta +1$.

Theorems & Definitions (13)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Lemma 1
• Theorem 1
• Definition 6
• Theorem 2
• Definition 7