The European sovereign debt crisis stands as the latest in a long line of similar crises. Argentina in 2001. Russia in 1998. Mexico in 1994. The list goes back into history. Debt crises are about as natural as earthquakes, but this time there is something different -- and possibly more dangerous.

The European nations are linked in a network of debts, as Bill Marsh recently illustrated in the New York Times with a beautiful piece of graphic art. Greece and Italy are prominent; Ireland, Portugal and Spain lurk ominously nearby. France and Germany seem exposed, too, as does the U.S.

The image is like a complex wiring diagram for a ticking debt bomb. Yet what it shows may be less important than what it leaves out: a largely invisible network of ties among institutions around the world, which could ultimately cause global financial chaos.

This hidden network has been created by institutions that buy and sell unregulated credit-default swaps. These are essentially insurance contracts on bonds; in the event of a default on the bond, the seller of the swap promises to pay the buyer the bond’s value.

Credit-default swaps are mostly arranged “over-the-counter,” not traded on any exchange or recorded by any central information repository. This explains why Marsh’s map couldn’t show the links they create.

But these undisclosed ties matter a lot. They were the primary reason the U.S. government needed to intervene in 2008 to prevent the collapse of insurance giant American International Group Inc. Ignoring the looming trouble with subprime mortgages, AIG had blithely sold CDS contracts insuring mortgage-backed securities to Goldman Sachs Group Inc., Societe Generale SA, Deutsche Bank AG and other firms. Suddenly, AIG was potentially on the hook for almost half a trillion dollars in payments. Through CDS contracts, AIG’s failure could have spread distress throughout the global financial system.

The AIG case illustrates an important paradox that looms again in today’s European debt crisis. Like regular insurance, credit-default swaps offer a way to spread risks, and standard thinking in economics holds that “risk sharing” of this kind should make individual banks safer, and the entire banking system more stable. It isn’t true, though, at least not always. In fact, too much sharing of risks can actually create bigger problems.

This follows from a recent study by Italian physicist Stefano Battiston and colleagues (one of whom is the Columbia University economist Joseph Stiglitz, winner of the 2001 Nobel Memorial Prize in Economic Sciences). The researchers showed that too much risk sharing can make it easy for distress to spread like a virus.

As part of normal business, each institution faces occasional “shocks” -- threats to financial health stemming from loans made to failed businesses and the like. A firm’s ability to withstand such shocks reflects its financial resilience. But an institution’s sturdiness also depends on the resilience of its trading partners, because if one of them gets into trouble, its distress will spread to others to whom it owes money.

Within this schematic of the banking system, Battiston and colleagues studied the likely consequences of the sudden bankruptcy of one institution, and specifically, how what happens depends on the overall “connectivity” in the network -- the density of risk-sharing connections.

They found that when the connectivity is relatively low, if one bank suddenly goes bankrupt, the repercussions aren’t so serious; the failure causes problems for a few other institutions but doesn’t generally propagate too far. In such a case, the risk-sharing is beneficial, just as the economics textbooks say it should be. Contracts like credit-default swaps can indeed bring benefits.

However, with rising connectivity -- as webs of CDS contracts grow more dense, for example -- things change dramatically. Beyond a certain connectivity threshold, attempts to share risk actually increase the likelihood that a bank will go under.

So many pathways are created along which trouble can spread that system-wide collapse becomes more likely. The web of risk-sharing connections within which an institution operates only gives an illusion of security.

This isn’t the kind of insight you can get just by sitting and thinking carefully; it’s revealed only with detailed analysis backed by computer simulations. (Further description of some of the technical details can be found on my blog.) Yes, it’s a little abstract; but so are the economic analyses suggesting that risk-sharing is always beneficial. Battiston and his colleagues’ analysis provides a global perspective that policy makers sorely need.

Companies that sell credit-default swaps argue that they do reduce risks, and many of their arguments are convincing. For example, international banks making loans to banks or corporations in a particular country may buy swaps on sovereign debt to protect themselves from systemic economic turmoil in that country. The possibility of protection encourages lending.

But there are limits. What reduces risk for individual institutions in small quantities spells trouble for the larger banking system when pushed too far. This is especially worrying when you consider that the number of CDS contracts outstanding on European sovereign debt has doubled in only the past three years, even after the AIG catastrophe. We don’t know if similar dangers lurk in the network of CDS contracts that links European banks with one another, as well as with banks in the U.S. and elsewhere.

Last year, writing in the Financial Times, former Federal Reserve Chairman Alan Greenspan said, “U.S. regulatory agencies will in the coming months be bedeviled by unanticipated adverse outcomes as they translate the Dodd-Frank Act’s broad set of principles into a couple of hundred detailed regulations.”

He’s certainly right that actions can have unanticipated consequences. Yet standing still and failing to regulate is also an action, which itself may entail unintended adverse outcomes. The explosion of unregulated and largely hidden CDS contracts was made possible by financial deregulation in 2000, and it has made the financial system more risky. Their unrestrained use -- especially with little knowledge of who is doing what -- looks like a recipe for disaster.

(Mark Buchanan is a physicist and the author of “The Social Atom: Why the Rich Get Richer, Cheaters Get Caught and Your Neighbor Usually Looks Like You,” is a Bloomberg View columnist. The opinions expressed are his own.)

To contact the writer of this article: Mark Buchanan at buchanan.mark@gmail.com.

To contact the editor responsible for this article: Mary Duenwald at mduenwald@bloomberg.net.