It’s shocking what you can learn from your own email inbox: You’re slow to reply to Mom, you’re losing touch with a close friend, and you and your spouse often discuss the same old topics. If only these revelations could be used to help you organize your inbox.

This week, I tested Cloze, a free Apple iOS app that prides itself on being an inbox-analyzing expert. Cloze uses an algorithm to study emails and other social-network interactions, then sorts messages according to who sent them, prioritizing those from people it thinks matter most to you.

I tested Cloze on an iPad, an iPhone and the Cloze website. (An Android app is planned for later this year.) Its people-focused concept is smart, and everyone wants a better way to manage inbox clutter. By incorporating social-network interactions, like those from Facebook, Twitter and LinkedIn, Cloze makes sure messages from important people don’t slip through the cracks.

It’s a pleasure to use because of its minimalistic layout with a lot of white space, which never felt overwhelming—no matter how many new messages or posts I received.

Cloze will even rate the electronic relationships you have with people, depending on several factors. I had fun sorting through people to see my Cloze Score with them. Cloze scores six categories for each person: Dormancy, Frequency, Responsiveness, Privacy, Freshness and Balance. I learned my mother-in-law and I have a well-balanced relationship, with a Balance score of 82 out of 100. My husband and I only got a 41 in Freshness, which means we could stand to talk about different topics more often. Then again, Cloze can’t track the conversations he and I have in person every day. In some cases of friends who I talk with mostly on the phone, scores didn’t accurately represent relationships.

The different list options on an iPhone.

After a week, I found myself wanting to check Cloze several times daily. But it was hard to stop checking my more familiar email and social-network programs first. Once an email message is read on Cloze, it can be automatically marked as read in one’s real inbox, but Twitter and Facebook posts were often replicated in both places. Yahoo, Exchange, iCloud Mail and AOL email are supported by Cloze, but not POP email accounts, like Outlook.com (formerly Hotmail).

One of my favorite aspects of Cloze is how it made me feel in control of my correspondence with close friends and family. A group called Key People is created after Cloze finishes analyzing your inbox and social networks. In my case, this analysis took about two hours and included one Gmail inbox and my Facebook and Twitter accounts. My Key People list accurately represented 25 people who mean a lot to me, and I added others manually (it holds up to 100). Once this was set up, the number of unread messages appeared beside this list. Cloze’s aim is to help you get that number to zero.

To do that, I chose actions for each. These actions depend on the message: Email options include Reply, Reply All and Forward; a tweet includes Reply, Retweet, Favorite or Email the person who posted it. A clever tree branch icon appears with each message and can be tapped to see a fan-like display of actions.

Even if you don’t know what to do with a message, you can still do something: Each message has a small bookmark in its top right corner that, when tapped, displays options that include Now, Today, Tomorrow and Next Week. I really liked this aspect of Cloze because I’m often in a rush and can’t handle a message at the moment its sent, but I want a way of reminding myself to follow up.

An automatically generated list called Losing Touch points out long- or short-term relationships that have started to fade. For example, Cloze understands if someone is considered a long-term relationship even though you haven’t received inbound communication in about two to four weeks. Key People get sorted into Losing Touch faster than others and stay in the Losing Touch list for longer.

Other lists can quickly be manually created and friends can be added to them with a simple tap. This is helpful if you want to organize groups of people or all correspondence associated with one particular thing, like buying a new house.

Cloze is happy to share with you all sorts of tidbits it has about your social interactions. It will even give you tips in a side panel about what helps make good relationships, like “Relationships need depth, but they also need to evolve.” Some people, though, could understandably be creeped out by the thought of getting relationship advice from an algorithm.

If you’re hoping to improve a relationship with someone, you can set a Cloze Score goal for your relationship to move that person’s emails and social-network posts to a higher priority in the list where they’re displayed. It won’t automatically move them to Key People. On the other hand, if someone is too noisy, posting lots of tweets and Facebook updates, you can tap a button to mute him or her; on the Cloze Web app, this muting can be adjusted to do things like just seeing direct messages and emails, not social-network posts.

There’s a lot of data stored up in your email inboxes and social-network interactions and Cloze reveals all of this in an easy-to-digest, stylish interface. But it’s tough to break the habit of looking at email, Facebook and Twitter the traditional way.

Write to Katie at katie.boehret@wsj.com

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