Is the US State of Delaware considered a southern state?

No. If you go by the definition of "southern" as states south of the Mason-Dixon Line, then Delaware was considered a northern state.

https://en.wikipedia.org/wiki/Mason-dixon_line

Yea, I saw that. But if you look at my link and scroll down to the 3rd pic it says different.

https://en.wikipedia.org/wiki/Southern_United_States

Modern definition: The states in dark red (see map) are almost always included in modern day definitions of the South, while those in medium red are usually included. Some sources classify Maryland and Missouri as Southern, with Delaware only rarely grouped within the region. West Virginia is often considered Southern, because it was once part of Virginia.

https://en.wikipedia.org/wiki/Southern_United_States

Your map is from the U.S. Census Bureau: THE SOUTH ATLANTIC STATES: Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, West Virginia, and Delaware

(Wiki links)

Delaware is a Border state.

https://en.wikipedia.org/wiki/Border_states_(American_Civil_War)

No, neither today nor historically has Delaware been grouped with the southern states.

If we consider the Confederate States of America to be "southern" and the remaining United States of America to be "northern," Delaware was a northern state during the Civil War, from which all the dust still hasn't quite settled.

As noted by star, Delaware was a "border" state, and a slaveholding one. But it stayed in the Union.

https://en.wikipedia.org/wiki/Confederate_States_of_America#Seceding_states
https://en.wikipedia.org/wiki/Union_%28American_Civil_War%29#Union_states

Today, it's called a "Mid-Atlantic" or "Middle Atlantic" state by most geographers and government agencies.
http://usa.usembassy.de/travel-regions.htm

I guess the bottom line here is it depends on the purpose. If you go by slave state versus free state, it is southern. If you go by on which side they fought during the Civil War, then it's northern. If you go by Census geographic regions, it's southern. If you talk to most southerns, they'll tell you it's northern.