In this Chief Marketing Technologist Blog ( guest post by Tyler Foxworthy, chief scientist at DemandJump, several fields of math are connected to marketing challenges that are being addressed with artificial intelligence. Editor Scott Brinkler also added several links to Wikipedia pages for readers who want to geek out like him on this dense and challenging topic.

The field of network science, which is rooted in statistical physics and graph theory, has emerged in recent years to help us understand how complex networks such as the internet form and evolve over time.

Social networks, the financial system, airlines, communication systems, the Internet — these complex networks are the substrate and substance of modern life.

Networks such as the Internet form following a process referred to as preferential attachment, whereby the competitive dynamics of the free market influence the topology of the internet like a glacier cuts a valley through a mountain range.

Preferential attachment is often referred to as “the rich get richer” phenomena — i.e., the more popular a node in a network (e.g., domains, websites, social influencers), the more likely it is that a newcomer to the network will want to link to it.

Over time, preferential attachment results in clustering among related web pages in a way that makes modern search engines possible. Data-driven marketers recognize these clusters as competitive ecosystems. Arguably, the reason Google succeeded, where earlier search engines failed, was due to their innovative understanding of the topology of scale-free networks.

The proliferation of marketing data and rapid advances in hardware allow marketers to map and measure the dynamics of their market ecosystems. The methods of network science allow them to comprehend it.

A holistic, network-level understanding of a marketing ecosystem provides countless benefits for marketers, and, in fact, will alter the course of marketing indefinitely. This represents a critical opportunity for marketers to shift away from last-click attribution and other simplistic models. Today, marketers can identify which nodes (domains, websites, social influencers) are affecting traffic and revenue — multiple steps before customers reach the domains of them or their competitors.

Graph theoretic methods enable savvy marketers to not only construct highly accurate maps of their market, but to track competitors, identify exactly where wins and losses occur, and predict where the greatest revenue opportunities can be captured.

It’s the difference between the first cartographers trying to map the geography of the Earth, and the 2000+ satellites that orbit our planet today. Having a holistic, network-level view, allows us to understand our surroundings with exponential precision.

Holistic Networks in Marketing

When coupled with artificial intelligence techniques such as reinforcement learning, these methods lead to strategies that optimize budget allocation and, ultimately, drive revenue.

Click here to read the full guest post on including the conclusion and the following expanded sections: